1 /* specfunc/test_legendre.c
3 * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2004 Gerard Jungman
5 * This program is free software; you can redistribute it and/or modify
6 * it under the terms of the GNU General Public License as published by
7 * the Free Software Foundation; either version 3 of the License, or (at
8 * your option) any later version.
10 * This program is distributed in the hope that it will be useful, but
11 * WITHOUT ANY WARRANTY; without even the implied warranty of
12 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 * General Public License for more details.
15 * You should have received a copy of the GNU General Public License
16 * along with this program; if not, write to the Free Software
17 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
20 /* Author: G. Jungman */
23 #include <gsl/gsl_test.h>
24 #include <gsl/gsl_sf.h>
28 int test_legendre(void)
31 double L[256], DL[256];
35 TEST_SF(s, gsl_sf_legendre_P1_e, (-0.5, &r), -0.5, TEST_TOL0, GSL_SUCCESS);
36 TEST_SF(s, gsl_sf_legendre_P1_e, ( 0.5, &r), 0.5, TEST_TOL0, GSL_SUCCESS);
38 TEST_SF(s, gsl_sf_legendre_P2_e, (0.0, &r), -0.5 , TEST_TOL0, GSL_SUCCESS);
39 TEST_SF(s, gsl_sf_legendre_P2_e, (0.5, &r), -0.125, TEST_TOL0, GSL_SUCCESS);
40 TEST_SF(s, gsl_sf_legendre_P2_e, (1.0, &r), 1.0 , TEST_TOL0, GSL_SUCCESS);
41 TEST_SF(s, gsl_sf_legendre_P2_e, (100.0, &r), 14999.5 , TEST_TOL0, GSL_SUCCESS);
43 TEST_SF(s, gsl_sf_legendre_P3_e, ( -0.5, &r), 0.4375, TEST_TOL0, GSL_SUCCESS);
44 TEST_SF(s, gsl_sf_legendre_P3_e, ( 0.5, &r), -0.4375, TEST_TOL0, GSL_SUCCESS);
45 TEST_SF(s, gsl_sf_legendre_P3_e, ( 1.0, &r), 1.0 , TEST_TOL0, GSL_SUCCESS);
46 TEST_SF(s, gsl_sf_legendre_P3_e, (100.0, &r), 2.49985e+06, TEST_TOL0, GSL_SUCCESS);
49 TEST_SF(s, gsl_sf_legendre_Pl_e, (1, -0.5, &r), -0.5, TEST_TOL0, GSL_SUCCESS);
50 TEST_SF(s, gsl_sf_legendre_Pl_e, (1, 1.0e-8, &r), 1.0e-08, TEST_TOL0, GSL_SUCCESS);
51 TEST_SF(s, gsl_sf_legendre_Pl_e, (1, 0.5, &r), 0.5, TEST_TOL0, GSL_SUCCESS);
52 TEST_SF(s, gsl_sf_legendre_Pl_e, (1, 1.0, &r), 1.0, TEST_TOL0, GSL_SUCCESS);
54 TEST_SF(s, gsl_sf_legendre_Pl_e, (10, -0.5, &r), -0.1882286071777345, TEST_TOL0, GSL_SUCCESS);
55 TEST_SF(s, gsl_sf_legendre_Pl_e, (10, 1.0e-8, &r), -0.24609374999999864648, TEST_TOL0, GSL_SUCCESS);
56 TEST_SF(s, gsl_sf_legendre_Pl_e, (10, 0.5, &r), -0.18822860717773437500, TEST_TOL0, GSL_SUCCESS);
57 TEST_SF(s, gsl_sf_legendre_Pl_e, (10, 1.0, &r), 1.0, TEST_TOL0, GSL_SUCCESS);
59 TEST_SF(s, gsl_sf_legendre_Pl_e, (99, -0.5, &r), 0.08300778172138770477, TEST_TOL0, GSL_SUCCESS);
60 TEST_SF(s, gsl_sf_legendre_Pl_e, (99, 1.0e-8, &r), -7.958923738716563193e-08, TEST_TOL0, GSL_SUCCESS);
61 TEST_SF(s, gsl_sf_legendre_Pl_e, (99, 0.5, &r), -0.08300778172138770477, TEST_TOL0, GSL_SUCCESS);
62 TEST_SF(s, gsl_sf_legendre_Pl_e, (99, 0.999, &r), -0.3317727359254778874, TEST_TOL2, GSL_SUCCESS);
63 TEST_SF(s, gsl_sf_legendre_Pl_e, (99, 1.0, &r), 1.0, TEST_TOL0, GSL_SUCCESS);
65 TEST_SF(s, gsl_sf_legendre_Pl_e, (1000, -0.5, &r), -0.019168251091650277878, TEST_TOL2, GSL_SUCCESS);
66 TEST_SF(s, gsl_sf_legendre_Pl_e, (1000, 1.0e-8, &r), 0.0252250181770982897470252620, TEST_TOL2, GSL_SUCCESS);
67 TEST_SF(s, gsl_sf_legendre_Pl_e, (1000, 0.5, &r), -0.019168251091650277878, TEST_TOL2, GSL_SUCCESS);
68 TEST_SF(s, gsl_sf_legendre_Pl_e, (1000, 1.0, &r), 1.0, TEST_TOL0, GSL_SUCCESS);
70 TEST_SF(s, gsl_sf_legendre_Pl_e, (4000, -0.5, &r), -0.009585404456573080972, TEST_TOL2, GSL_SUCCESS);
71 TEST_SF(s, gsl_sf_legendre_Pl_e, (4000, 0.5, &r), -0.009585404456573080972, TEST_TOL2, GSL_SUCCESS);
72 TEST_SF(s, gsl_sf_legendre_Pl_e, (4000, 1.0, &r), 1.0, TEST_TOL0, GSL_SUCCESS);
75 gsl_sf_legendre_Pl_array(100, 0.5, L);
76 TEST_SF_VAL(sa, L[0], +0.0, 1.0, TEST_TOL1);
77 TEST_SF_VAL(sa, L[10], +0.0, -0.18822860717773437500, TEST_TOL1);
78 TEST_SF_VAL(sa, L[100], +0.0, -0.06051802596186118687, TEST_TOL1);
79 gsl_test(sa, "gsl_sf_legendre_Pl_array(100, 0.5)");
83 gsl_sf_legendre_Pl_deriv_array(100, 0.5, L, DL);
84 TEST_SF_VAL(sa, DL[0], +0.0, 0.0, TEST_TOL1);
85 TEST_SF_VAL(sa, DL[1], +0.0, 1.0, TEST_TOL1);
86 TEST_SF_VAL(sa, DL[10], +0.0, -2.3171234130859375000, TEST_TOL1);
87 TEST_SF_VAL(sa, DL[100], +0.0, -7.0331691653942815112, TEST_TOL1);
88 gsl_test(sa, "gsl_sf_legendre_Pl_deriv_array(100, 0.5)");
92 gsl_sf_legendre_Pl_deriv_array(10, 1.0, L, DL);
93 TEST_SF_VAL(sa, DL[0], +0.0, 0.0, TEST_TOL1);
94 TEST_SF_VAL(sa, DL[1], +0.0, 1.0, TEST_TOL1);
95 TEST_SF_VAL(sa, DL[10], +0.0, 55.0, TEST_TOL1);
96 gsl_test(sa, "gsl_sf_legendre_Pl_deriv_array(10, 1.0)");
99 gsl_sf_legendre_Pl_deriv_array(10, 1.0 - 1.0e-11, L, DL);
100 TEST_SF_VAL(sa, DL[0], +0.0, 0.0, TEST_TOL1);
101 TEST_SF_VAL(sa, DL[1], +0.0, 1.0, TEST_TOL1);
102 TEST_SF_VAL(sa, DL[10], +0.0, 54.999999985150000001, TEST_TOL1);
103 gsl_test(sa, "gsl_sf_legendre_Pl_deriv_array(10, 1.0 - 1.0e-11)");
106 gsl_sf_legendre_Pl_deriv_array(10, -1.0, L, DL);
107 TEST_SF_VAL(sa, DL[0], +0.0, 0.0, TEST_TOL1);
108 TEST_SF_VAL(sa, DL[1], +0.0, 1.0, TEST_TOL1);
109 TEST_SF_VAL(sa, DL[10], +0.0, -55.0, TEST_TOL1);
110 gsl_test(sa, "gsl_sf_legendre_Pl_deriv_array(10, -1.0)");
113 gsl_sf_legendre_Pl_deriv_array(10, -1.0 + 1.0e-11, L, DL);
114 TEST_SF_VAL(sa, DL[0], +0.0, 0.0, TEST_TOL1);
115 TEST_SF_VAL(sa, DL[1], +0.0, 1.0, TEST_TOL1);
116 TEST_SF_VAL(sa, DL[10], +0.0, -54.999999985150000001, TEST_TOL1);
117 gsl_test(sa, "gsl_sf_legendre_Pl_deriv_array(10, -1.0 + 1.0e-11)");
121 TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 0, -0.5, &r), -0.18822860717773437500, TEST_TOL0, GSL_SUCCESS);
122 TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 0, 1.0e-08, &r), -0.24609374999999864648, TEST_TOL0, GSL_SUCCESS);
123 TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 0, 0.5, &r), -0.18822860717773437500, TEST_TOL0, GSL_SUCCESS);
125 TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 1, -0.5, &r), -2.0066877394361256516, TEST_TOL0, GSL_SUCCESS);
126 TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 1, 1.0e-08, &r), -2.7070312499999951725e-07, TEST_TOL0, GSL_SUCCESS);
127 TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 1, 0.5, &r), 2.0066877394361256516, TEST_TOL0, GSL_SUCCESS);
129 TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 5, -0.5, &r), -30086.169706116174977, TEST_TOL0, GSL_SUCCESS);
130 TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 5, 1.0e-08, &r), -0.0025337812499999964949, TEST_TOL0, GSL_SUCCESS);
131 TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 5, 0.5, &r), 30086.169706116174977, TEST_TOL0, GSL_SUCCESS);
132 TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 5, 0.999, &r), -0.5036411489013270406, TEST_TOL1, GSL_SUCCESS);
134 TEST_SF(s, gsl_sf_legendre_Plm_e, (100, 5, -0.5, &r), -6.617107444248382171e+08, TEST_TOL0, GSL_SUCCESS);
135 TEST_SF(s, gsl_sf_legendre_Plm_e, (100, 5, 1.0e-08, &r), 817.8987598063712851, TEST_TOL0, GSL_SUCCESS);
136 TEST_SF(s, gsl_sf_legendre_Plm_e, (100, 5, 0.5, &r), 6.617107444248382171e+08, TEST_TOL0, GSL_SUCCESS);
137 TEST_SF(s, gsl_sf_legendre_Plm_e, (100, 5, 0.999, &r), -1.9831610803806212189e+09, TEST_TOL2, GSL_SUCCESS);
141 gsl_sf_legendre_Plm_deriv_array(100, 2, -1.0 + 1.0/1125899906842624.0, L, DL);
142 TEST_SF_VAL(sa, L[0], +0.0, 5.3290705182007490275e-15, TEST_TOL1);
143 TEST_SF_VAL(sa, L[1], +0.0, -2.6645352591003721471e-14, TEST_TOL1);
144 TEST_SF_VAL(sa, L[98], +0.0, 2.2646284847349109694e-08, TEST_TOL2);
145 gsl_test(sa, "gsl_sf_legendre_Plm_deriv_array(100, 2, -1.0 + 2^(-50)");
149 gsl_sf_legendre_Plm_deriv_array(100, 2, 1.0 - 1.0/1125899906842624.0, L, DL);
150 TEST_SF_VAL(sa, L[0], +0.0, 5.3290705182007490275e-15, TEST_TOL1);
151 TEST_SF_VAL(sa, L[1], +0.0, 2.6645352591003721471e-14, TEST_TOL1);
152 TEST_SF_VAL(sa, L[10], +0.0, 5.3343995887188313290e-12, TEST_TOL1);
153 TEST_SF_VAL(sa, L[98], +0.0, 2.2646284847349109694e-08, TEST_TOL2);
154 gsl_test(sa, "gsl_sf_legendre_Plm_deriv_array(100, 2, 1.0 - 2^(-50)");
158 gsl_sf_legendre_Plm_array(100, 5, 0.5, L);
159 TEST_SF_VAL(sa, L[0], +0.0, -460.3466286991656682, TEST_TOL1);
160 TEST_SF_VAL(sa, L[10], +0.0, 38852.51334152290535, TEST_TOL1 );
161 TEST_SF_VAL(sa, L[95], +0.0, 6.617107444248382171e+08, TEST_TOL1);
162 gsl_test(sa, "gsl_sf_legendre_Plm_array(100, 5, 0.5)");
166 gsl_sf_legendre_Plm_array(100, 5, 0.999, L);
167 TEST_SF_VAL(sa, L[0], +0.0, -0.00016883550990916552255, TEST_TOL2);
168 TEST_SF_VAL(sa, L[10], +0.0, -30.651334850159821525, TEST_TOL2 );
169 TEST_SF_VAL(sa, L[95], +0.0, -1.9831610803806212189e+09, TEST_TOL2);
170 gsl_test(sa, "gsl_sf_legendre_Plm_array(100, 5, 0.999)");
174 gsl_sf_legendre_Plm_array(100, 5, -0.999, L);
175 TEST_SF_VAL(sa, L[0], +0.0, -0.00016883550990916552255, TEST_TOL2);
176 TEST_SF_VAL(sa, L[10], +0.0, -30.651334850159821525, TEST_TOL2 );
177 TEST_SF_VAL(sa, L[95], +0.0, 1.9831610803806212189e+09, TEST_TOL2);
178 gsl_test(sa, "gsl_sf_legendre_Plm_array(100, 5, -0.999)");
182 gsl_sf_legendre_Plm_deriv_array(100, 2, 0.999, L, DL);
183 TEST_SF_VAL(sa, L[0], +0.0, 0.00599700000000000000, TEST_TOL1);
184 TEST_SF_VAL(sa, L[1], +0.0, 0.02995501500000000000, TEST_TOL1 );
185 TEST_SF_VAL(sa, DL[0], +0.0, -5.9940000000000000000, TEST_TOL1);
186 TEST_SF_VAL(sa, DL[1], +0.0, -29.910045000000000000, TEST_TOL1 );
187 TEST_SF_VAL(sa, DL[2], +0.0, -89.490629790000000000, TEST_TOL1 );
188 TEST_SF_VAL(sa, DL[10], +0.0, -5703.9461633355291972, TEST_TOL1 );
189 TEST_SF_VAL(sa, DL[95], +0.0, 6.4518473603456858414E+06, TEST_TOL3);
190 gsl_test(sa, "gsl_sf_legendre_Plm_deriv_array(100, 2, 0.999)");
194 gsl_sf_legendre_Plm_deriv_array(100, 2, 1.0 - 1.0e-15, L, DL);
195 TEST_SF_VAL(sa, DL[0], +0.0, -5.9999999999999940000, TEST_TOL1);
196 TEST_SF_VAL(sa, DL[1], +0.0, -29.999999999999910000, TEST_TOL1 );
197 TEST_SF_VAL(sa, DL[2], +0.0, -89.999999999999490000, TEST_TOL1 );
198 TEST_SF_VAL(sa, DL[10], +0.0, -6005.9999999996936940, TEST_TOL1 );
199 TEST_SF_VAL(sa, DL[95], +0.0, -2.2586255999928454270e+07, TEST_TOL3);
200 gsl_test(sa, "gsl_sf_legendre_Plm_deriv_array(100, 2, 1.0 - 1.0e-15)");
204 gsl_sf_legendre_Plm_deriv_array(100, 2, -1.0 + 1.0e-15, L, DL);
205 TEST_SF_VAL(sa, DL[0], +0.0, 5.9999999999999940000, TEST_TOL1);
206 TEST_SF_VAL(sa, DL[1], +0.0, -29.999999999999910000, TEST_TOL1 );
207 TEST_SF_VAL(sa, DL[95], +0.0, -2.2586255999928454270e+07, TEST_TOL3);
208 gsl_test(sa, "gsl_sf_legendre_Plm_deriv_array(100, 2, -1.0 + 1.0e-15)");
212 gsl_sf_legendre_Plm_deriv_array(100, 5, 0.999, L, DL);
213 TEST_SF_VAL(sa, DL[0], +0.0, 0.42187762481054616565, TEST_TOL1);
214 TEST_SF_VAL(sa, DL[1], +0.0, 4.6341560284340909936, TEST_TOL1 );
215 TEST_SF_VAL(sa, DL[2], +0.0, 27.759505566959219127, TEST_TOL1 );
216 TEST_SF_VAL(sa, DL[10], +0.0, 76051.795860179545484, TEST_TOL1 );
217 TEST_SF_VAL(sa, DL[95], +0.0, 3.0344503083851936814e+12, TEST_TOL3);
218 gsl_test(sa, "gsl_sf_legendre_Plm_deriv_array(100, 5, 0.999)");
221 TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 0, -0.5, &r), -0.24332702369300133776, TEST_TOL0, GSL_SUCCESS);
222 TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 0, 0.5, &r), -0.24332702369300133776, TEST_TOL0, GSL_SUCCESS);
223 TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 0, 0.999, &r), 1.2225754122797385990, TEST_TOL1, GSL_SUCCESS);
225 TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 5, -0.5, &r), -0.3725739049803293972, TEST_TOL0, GSL_SUCCESS);
226 TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 5, 1.0e-08, &r), -3.1377233589376792243e-08, TEST_TOL0, GSL_SUCCESS);
227 TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 5, 0.5, &r), 0.3725739049803293972, TEST_TOL0, GSL_SUCCESS);
228 TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 5, 0.999, &r), -6.236870674727370094e-06, TEST_TOL2, GSL_SUCCESS);
230 TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 10, -0.5, &r), 0.12876871185785724117, TEST_TOL1, GSL_SUCCESS);
231 TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 10, 0.5, &r), 0.12876871185785724117, TEST_TOL1, GSL_SUCCESS);
232 TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 10, 0.999, &r), 1.7320802307583118647e-14, TEST_TOL2, GSL_SUCCESS);
234 TEST_SF(s, gsl_sf_legendre_sphPlm_e, (200, 1, -0.5, &r), 0.3302975570099492931, TEST_TOL1, GSL_SUCCESS);
235 TEST_SF(s, gsl_sf_legendre_sphPlm_e, (200, 1, 0.5, &r), -0.3302975570099492931, TEST_TOL1, GSL_SUCCESS);
236 TEST_SF(s, gsl_sf_legendre_sphPlm_e, (200, 1, 0.999, &r), -1.4069792055546256912, TEST_TOL2, GSL_SUCCESS);
240 /* Test case from alberto@physik.fu-berlin.de */
242 TEST_SF(s, gsl_sf_legendre_sphPlm_e, (3, 1, 0.0, &r), 0.323180184114150653007, TEST_TOL2, GSL_SUCCESS);
244 /* Other test cases */
246 TEST_SF(s, gsl_sf_legendre_sphPlm_e, (200, 1, -0.5, &r), 0.3302975570099492931418227583, TEST_TOL2, GSL_SUCCESS);
247 TEST_SF(s, gsl_sf_legendre_sphPlm_e, (140,135,1,&r), 0.0, TEST_TOL2, GSL_SUCCESS);
250 TEST_SF(s, gsl_sf_legendre_sphPlm_e, (140,135,0.99998689456491752,&r), -6.54265253269093276310395668335e-305, TEST_TOL6, GSL_SUCCESS);
254 gsl_sf_legendre_sphPlm_array(100, 5, 0.5, L);
255 TEST_SF_VAL(sa, L[0], +0.0, -0.22609703187800460722, TEST_TOL1);
256 TEST_SF_VAL(sa, L[10], +0.0, 0.07452710323813558940, TEST_TOL1);
257 TEST_SF_VAL(sa, L[95], +0.0, 0.25865355990880161717, TEST_TOL1);
258 gsl_test(sa, "gsl_sf_legendre_sphPlm_array(100, 5, 0.5)");
262 gsl_sf_legendre_sphPlm_array(100, 2, 1.0 - 1.0/1125899906842624.0, L);
263 TEST_SF_VAL(sa, L[0], +0.0, 6.8616082064776657177e-16, TEST_TOL2);
264 TEST_SF_VAL(sa, L[10], +0.0, 4.8543150313086787324e-14, TEST_TOL2);
265 TEST_SF_VAL(sa, L[95], +0.0, 8.3138984963650838973e-12, TEST_TOL2);
266 gsl_test(sa, "gsl_sf_legendre_sphPlm_array(100, 2, 1.0 - 2^(-50))");
270 gsl_sf_legendre_sphPlm_array(100, 2, -1.0 + 1.0/1125899906842624.0, L);
271 TEST_SF_VAL(sa, L[0], +0.0, 6.8616082064776657177e-16, TEST_TOL2);
272 TEST_SF_VAL(sa, L[95], +0.0, -8.3138984963650838973e-12, TEST_TOL2);
273 gsl_test(sa, "gsl_sf_legendre_sphPlm_array(100, 2, -1.0 + 2^(-50))");
277 gsl_sf_legendre_sphPlm_deriv_array(100, 0, 0.5, L, DL);
278 TEST_SF_VAL(sa, DL[0], +0.0, 0.0, TEST_TOL1);
279 TEST_SF_VAL(sa, DL[10], +0.0, -2.9953934850252897591, TEST_TOL1);
280 TEST_SF_VAL(sa, DL[95], +0.0, -36.411811015111761007, TEST_TOL1);
281 gsl_test(sa, "gsl_sf_legendre_sphPlm_deriv_array(100, 0, 0.5)");
285 gsl_sf_legendre_sphPlm_deriv_array(100, 1, 0.5, L, DL);
286 TEST_SF_VAL(sa, DL[0], +0.0, 0.19947114020071633897, TEST_TOL1);
287 TEST_SF_VAL(sa, DL[1], +0.0, -0.44603102903819277863, TEST_TOL1);
288 TEST_SF_VAL(sa, DL[10], +0.0, 1.3658895325030216565, TEST_TOL1);
289 TEST_SF_VAL(sa, DL[99], +0.0, -27.925571865639037118, TEST_TOL1);
290 gsl_test(sa, "gsl_sf_legendre_sphPlm_deriv_array(100, 1, 0.5)");
294 gsl_sf_legendre_sphPlm_deriv_array(100, 1, 1.0 - 1.0/1125899906842624.0, L, DL);
295 TEST_SF_VAL(sa, DL[0], +0.0, 8.1973898803378530946e+06, TEST_TOL1);
296 TEST_SF_VAL(sa, DL[1], +0.0, 1.8329921010504257405e+07, TEST_TOL1);
297 TEST_SF_VAL(sa, DL[10], +0.0, 1.8439572562895384115e+08, TEST_TOL1);
298 TEST_SF_VAL(sa, DL[99], +0.0, 4.7682463136232210552e+09, TEST_TOL3);
299 gsl_test(sa, "gsl_sf_legendre_sphPlm_deriv_array(100, 1, 1.0 - 2^(-50))");
303 gsl_sf_legendre_sphPlm_deriv_array(100, 2, 0.5, L, DL);
304 TEST_SF_VAL(sa, DL[0], +0.0, -0.38627420202318958034, TEST_TOL1);
305 TEST_SF_VAL(sa, DL[1], +0.0, 0.25549636910832059085, TEST_TOL1);
306 TEST_SF_VAL(sa, DL[2], +0.0, 1.5053547230039006279, TEST_TOL1);
307 TEST_SF_VAL(sa, DL[10], +0.0, 0.73576559668648243477, TEST_TOL1);
308 TEST_SF_VAL(sa, DL[98], +0.0, 28.444589950264378407, TEST_TOL1);
309 gsl_test(sa, "gsl_sf_legendre_sphPlm_deriv_array(100, 2, 0.5)");
313 gsl_sf_legendre_sphPlm_deriv_array(100, 5, 0.5, L, DL);
314 TEST_SF_VAL(sa, DL[0], +0.0, 0.75365677292668202407, TEST_TOL1);
315 TEST_SF_VAL(sa, DL[1], +0.0, 0.54346962777757450534, TEST_TOL1);
316 TEST_SF_VAL(sa, DL[2], +0.0, -0.98309969029001383773, TEST_TOL1);
317 TEST_SF_VAL(sa, DL[3], +0.0, -2.7728270988954534293, TEST_TOL1);
318 TEST_SF_VAL(sa, DL[10], +0.0, -5.7407133315443482193, TEST_TOL1);
319 TEST_SF_VAL(sa, DL[95], +0.0, -25.893934624747394561, TEST_TOL1);
320 gsl_test(sa, "gsl_sf_legendre_sphPlm_deriv_array(100, 5, 0.5)");
324 gsl_sf_legendre_sphPlm_deriv_array(100, 5, 1.0 - 1.0/1125899906842624.0, L, DL);
325 TEST_SF_VAL(sa, DL[0], +0.0, 1.7374288379067753301e-22, TEST_TOL1);
326 TEST_SF_VAL(sa, DL[1], +0.0, 6.2643887625426827113e-22, TEST_TOL1);
327 TEST_SF_VAL(sa, DL[2], +0.0, 1.6482697200734667281e-21, TEST_TOL1);
328 TEST_SF_VAL(sa, DL[95], +0.0, 3.9890549466071349506e-15, TEST_TOL2);
329 gsl_test(sa, "gsl_sf_legendre_sphPlm_deriv_array(100, 5, 1.0 - 2^(-50))");
332 gsl_sf_legendre_sphPlm_deriv_array(100, 5, -1.0 + 1.0/1125899906842624.0, L, DL);
333 TEST_SF_VAL(sa, DL[0], +0.0, -1.7374288379067753301e-22, TEST_TOL1);
334 TEST_SF_VAL(sa, DL[1], +0.0, 6.2643887625426827113e-22, TEST_TOL1);
335 TEST_SF_VAL(sa, DL[2], +0.0, -1.6482697200734667281e-21, TEST_TOL1);
336 TEST_SF_VAL(sa, DL[95], +0.0, 3.9890549466071349506e-15, TEST_TOL3);
337 gsl_test(sa, "gsl_sf_legendre_sphPlm_deriv_array(100, 5, -1.0 + 2^(-50))");
340 TEST_SF(s, gsl_sf_conicalP_half_e, (0.0, -0.5, &r), 0.8573827581049917129, TEST_TOL0, GSL_SUCCESS);
341 TEST_SF(s, gsl_sf_conicalP_half_e, (0.0, 0.5, &r), 0.8573827581049917129, TEST_TOL0, GSL_SUCCESS);
342 TEST_SF(s, gsl_sf_conicalP_half_e, (0.0, 2.0, &r), 0.6062611623284649811, TEST_TOL0, GSL_SUCCESS);
343 TEST_SF(s, gsl_sf_conicalP_half_e, (0.0, 100.0, &r), 0.07979045091636735635, TEST_TOL0, GSL_SUCCESS);
345 TEST_SF(s, gsl_sf_conicalP_half_e, (10.0, -0.5, &r), 5.345484922591867188e+08, TEST_TOL1, GSL_SUCCESS);
346 TEST_SF(s, gsl_sf_conicalP_half_e, (10.0, 0.5, &r), 15137.910380385258370, TEST_TOL1, GSL_SUCCESS);
347 TEST_SF(s, gsl_sf_conicalP_half_e, (10.0, 2.0, &r), 0.4992680691891618544, TEST_TOL1, GSL_SUCCESS);
348 TEST_SF(s, gsl_sf_conicalP_half_e, (10.0, 100.0, &r), -0.07272008163718195685, TEST_TOL2, GSL_SUCCESS);
350 TEST_SF(s, gsl_sf_conicalP_half_e, (200.0, -1.0e-3, &r), 1.3347639529084185010e+136, TEST_TOL2, GSL_SUCCESS);
351 TEST_SF(s, gsl_sf_conicalP_half_e, (200.0, 1.0e-8, &r), 1.0928098010940058507e+136, TEST_TOL2, GSL_SUCCESS);
352 TEST_SF(s, gsl_sf_conicalP_half_e, (200.0, 0.5, &r), 3.895546021611205442e+90, TEST_TOL2, GSL_SUCCESS);
353 TEST_SF(s, gsl_sf_conicalP_half_e, (200.0, 10.0, &r), -0.04308567180833581268, TEST_TOL3, GSL_SUCCESS);
354 TEST_SF(s, gsl_sf_conicalP_half_e, (200.0, 100.0, &r), -0.04694669186576399194, TEST_TOL3, GSL_SUCCESS);
355 TEST_SF(s, gsl_sf_conicalP_half_e, (200.0, 1000.0, &r), 0.023698140704121273277, TEST_TOL3, GSL_SUCCESS);
356 TEST_SF(s, gsl_sf_conicalP_half_e, (200.0, 1.0e+8, &r), -0.00006790983312124277891, TEST_TOL3, GSL_SUCCESS);
358 TEST_SF(s, gsl_sf_conicalP_half_e, (1.0e+8, 1.1, &r), 1.1599311133054742944, TEST_SQRT_TOL0, GSL_SUCCESS);
359 TEST_SF(s, gsl_sf_conicalP_half_e, (1.0e+8, 100.0, &r), 0.07971967557381557875, TEST_SQRT_TOL0, GSL_SUCCESS);
361 TEST_SF(s, gsl_sf_conicalP_mhalf_e, (0.0, -0.5, &r), 1.7956982494514644808, TEST_TOL0, GSL_SUCCESS);
362 TEST_SF(s, gsl_sf_conicalP_mhalf_e, (0.0, 0.5, &r), 0.8978491247257322404, TEST_TOL0, GSL_SUCCESS);
363 TEST_SF(s, gsl_sf_conicalP_mhalf_e, (0.0, 2.0, &r), 0.7984204253272901551, TEST_TOL0, GSL_SUCCESS);
364 TEST_SF(s, gsl_sf_conicalP_mhalf_e, (0.0, 100.0, &r), 0.4227531369388072584, TEST_TOL0, GSL_SUCCESS);
366 TEST_SF(s, gsl_sf_conicalP_mhalf_e, (10.0, -0.5, &r), 5.345484922591867181e+07, TEST_TOL1, GSL_SUCCESS);
367 TEST_SF(s, gsl_sf_conicalP_mhalf_e, (10.0, 0.5, &r), 1513.7910356104985334, TEST_TOL1, GSL_SUCCESS);
368 TEST_SF(s, gsl_sf_conicalP_mhalf_e, (10.0, 2.0, &r), 0.03439243987215615642, TEST_TOL1, GSL_SUCCESS);
369 TEST_SF(s, gsl_sf_conicalP_mhalf_e, (10.0, 100.0, &r), 0.003283756665952609624, TEST_TOL2, GSL_SUCCESS);
371 TEST_SF(s, gsl_sf_conicalP_mhalf_e, (200.0, -0.5, &r), 1.7699538115312304280e+179, TEST_TOL2, GSL_SUCCESS);
372 TEST_SF(s, gsl_sf_conicalP_mhalf_e, (200.0, 1.0e-8, &r), 5.464049005470029253e+133, TEST_TOL2, GSL_SUCCESS);
373 TEST_SF(s, gsl_sf_conicalP_mhalf_e, (200.0, 0.5, &r), 1.9477730108056027211e+88, TEST_TOL2, GSL_SUCCESS);
374 TEST_SF(s, gsl_sf_conicalP_mhalf_e, (200.0, 10.0, &r), 0.0012462575917716355362, TEST_TOL2, GSL_SUCCESS);
375 TEST_SF(s, gsl_sf_conicalP_mhalf_e, (200.0, 100.0, &r), -0.0003225881344802625149, TEST_TOL2, GSL_SUCCESS);
376 TEST_SF(s, gsl_sf_conicalP_mhalf_e, (200.0, 1000.0, &r), -0.00004330652890886567623, TEST_TOL3, GSL_SUCCESS);
377 TEST_SF(s, gsl_sf_conicalP_mhalf_e, (200.0, 1.0e+8, &r), 2.0943091278037078483e-07, TEST_TOL3, GSL_SUCCESS);
379 TEST_SF(s, gsl_sf_conicalP_mhalf_e, (1.0e+8, 1.1, &r), 2.092320445620989618e-09, 16.0*TEST_SQRT_TOL0, GSL_SUCCESS);
380 TEST_SF(s, gsl_sf_conicalP_mhalf_e, (1.0e+8, 100.0, &r), -3.359967833599016923e-11, 256.0*TEST_SQRT_TOL0, GSL_SUCCESS);
383 TEST_SF(s, gsl_sf_conicalP_0_e, (0.0, -0.5, &r), 1.3728805006183501647, TEST_TOL0, GSL_SUCCESS);
384 TEST_SF(s, gsl_sf_conicalP_0_e, (0.0, 0.5, &r), 1.0731820071493643751, TEST_TOL0, GSL_SUCCESS);
385 TEST_SF(s, gsl_sf_conicalP_0_e, (0.0, 2.0, &r), 0.9012862993604472987, TEST_TOL0, GSL_SUCCESS);
386 TEST_SF(s, gsl_sf_conicalP_0_e, (0.0, 100.0, &r), 0.30091748588199264556, TEST_TOL0, GSL_SUCCESS);
388 TEST_SF(s, gsl_sf_conicalP_0_e, (10.0, -0.5, &r), 1.6795592815421804669e+08, TEST_TOL1, GSL_SUCCESS);
389 TEST_SF(s, gsl_sf_conicalP_0_e, (10.0, 0.5, &r), 4826.034132009618240, TEST_TOL1, GSL_SUCCESS);
390 TEST_SF(s, gsl_sf_conicalP_0_e, (10.0, 2.0, &r), 0.18798468917758716146, TEST_TOL2, GSL_SUCCESS);
391 TEST_SF(s, gsl_sf_conicalP_0_e, (10.0, 100.0, &r), -0.008622130749987962529, TEST_TOL2, GSL_SUCCESS);
393 TEST_SF(s, gsl_sf_conicalP_0_e, (200.0, -0.5, &r), 2.502194818646823e+180, TEST_TOL4, GSL_SUCCESS);
395 TEST_SF(s, gsl_sf_conicalP_0_e, (1000.0, 100.0, &r), 0.0017908817653497715844, TEST_TOL3, GSL_SUCCESS);
396 TEST_SF(s, gsl_sf_conicalP_0_e, (1000.0, 1000.0, &r), -0.0006566893804926284301, TEST_TOL3, GSL_SUCCESS);
397 TEST_SF(s, gsl_sf_conicalP_0_e, (1000.0, 1.0e+8, &r), 2.3167213561756390068e-06, TEST_TOL4, GSL_SUCCESS);
399 TEST_SF(s, gsl_sf_conicalP_1_e, (0.0, -0.5, &r), 0.4939371126656998499, TEST_TOL1, GSL_SUCCESS);
400 TEST_SF(s, gsl_sf_conicalP_1_e, (0.0, 0.5, &r), 0.14933621085538265636, TEST_TOL1, GSL_SUCCESS);
401 TEST_SF(s, gsl_sf_conicalP_1_e, (0.0, 2.0, &r), -0.13666874968871549533, TEST_TOL1, GSL_SUCCESS);
402 TEST_SF(s, gsl_sf_conicalP_1_e, (0.0, 100.0, &r), -0.10544528203156629098, TEST_TOL2, GSL_SUCCESS);
404 TEST_SF(s, gsl_sf_conicalP_1_e, (10.0, -0.5, &r), 1.7253802958788312520e+09, TEST_TOL2, GSL_SUCCESS);
405 TEST_SF(s, gsl_sf_conicalP_1_e, (10.0, 0.5, &r), 46781.02294059967988, TEST_TOL1, GSL_SUCCESS);
406 TEST_SF(s, gsl_sf_conicalP_1_e, (10.0, 2.0, &r), 0.26613342643657444400, TEST_TOL2, GSL_SUCCESS);
407 TEST_SF(s, gsl_sf_conicalP_1_e, (10.0, 100.0, &r), -0.23281959695501029796, TEST_TOL2, GSL_SUCCESS);
410 /* FIXME: Mathematica gets some brain-damaged numbers for
411 * these x < 0 points. I have checked what I am doing in detail,
412 * and it must be right because you can do it by summing
413 * manifestly positive definite quantities.
415 TEST_SF(s, gsl_sf_conicalP_1_e, (200.0, -0.999, &r), 2.71635193199341135e+270, TEST_TOL2, GSL_SUCCESS);
416 TEST_SF(s, gsl_sf_conicalP_1_e, (200.0, -0.9, &r), 4.2952493176812905e+234, TEST_TOL2, GSL_SUCCESS);
417 TEST_SF(s, gsl_sf_conicalP_1_e, (200.0, -0.5, &r), 5.01159205956053439e+182, TEST_TOL3, GSL_SUCCESS);
418 TEST_SF(s, gsl_sf_conicalP_1_e, (200.0, 0.999, &r), 195733.0396081538, TEST_TOL2, GSL_SUCCESS);
419 TEST_SF(s, gsl_sf_conicalP_1_e, (200.0, 10.0, &r), -2.9272610662414349553, TEST_TOL2, GSL_SUCCESS);
421 TEST_SF(s, gsl_sf_conicalP_1_e, (1000.0, 100.0, &r), -1.7783258105862399857, TEST_TOL6, GSL_SUCCESS);
422 TEST_SF(s, gsl_sf_conicalP_1_e, (1000.0, 1000.0, &r), 0.4535161075156427179, TEST_TOL4, GSL_SUCCESS);
423 TEST_SF(s, gsl_sf_conicalP_1_e, (1000.0, 1.0e+8, &r), 0.0009983414549874888478, TEST_SQRT_TOL0, GSL_SUCCESS);
426 TEST_SF(s, gsl_sf_conicalP_sph_reg_e, (2, 1.0, -0.5, &r), 1.6406279287008789526, TEST_TOL0, GSL_SUCCESS);
427 TEST_SF(s, gsl_sf_conicalP_sph_reg_e, (10, 1.0, -0.5, &r), 0.000029315266725049129448, TEST_TOL1, GSL_SUCCESS);
428 TEST_SF(s, gsl_sf_conicalP_sph_reg_e, (20, 1.0, -0.5, &r), 7.335769429462034431e-15, TEST_TOL1, GSL_SUCCESS);
429 TEST_SF(s, gsl_sf_conicalP_sph_reg_e, (30, 1.0, -0.5, &r), 1.3235612394267378871e-26, TEST_TOL2, GSL_SUCCESS);
430 TEST_SF(s, gsl_sf_conicalP_sph_reg_e, (10, 1.0, 0.5, &r), 2.7016087199857873954e-10, TEST_TOL1, GSL_SUCCESS);
431 TEST_SF(s, gsl_sf_conicalP_sph_reg_e, (20, 1.0, 0.5, &r), 1.1782569701435933399e-24, TEST_TOL1, GSL_SUCCESS);
432 TEST_SF(s, gsl_sf_conicalP_sph_reg_e, (30, 1.0, 0.5, &r), 3.636240588303797919e-41, TEST_TOL1, GSL_SUCCESS);
433 TEST_SF(s, gsl_sf_conicalP_sph_reg_e, (10, 1.0, 2.0, &r), 2.4934929626284934483e-10, TEST_TOL1, GSL_SUCCESS);
434 TEST_SF(s, gsl_sf_conicalP_sph_reg_e, (20, 1.0, 2.0, &r), 1.1284762488012616191e-24, TEST_TOL2, GSL_SUCCESS);
435 TEST_SF(s, gsl_sf_conicalP_sph_reg_e, (30, 100.0, 100.0, &r), -1.6757772087159526048e-64, TEST_TOL6, GSL_SUCCESS);
438 TEST_SF(s, gsl_sf_conicalP_cyl_reg_e, (2, 1.0, -0.5, &r), 2.2048510472375258708, TEST_TOL0, GSL_SUCCESS);
439 TEST_SF(s, gsl_sf_conicalP_cyl_reg_e, (10, 1.0, -0.5, &r), 0.00007335034531618655690, TEST_TOL1, GSL_SUCCESS);
440 TEST_SF(s, gsl_sf_conicalP_cyl_reg_e, (20, 1.0, -0.5, &r), 2.5419860619212164696e-14, TEST_TOL1, GSL_SUCCESS);
441 TEST_SF(s, gsl_sf_conicalP_cyl_reg_e, (30, 1.0, -0.5, &r), 5.579714972260536827e-26, TEST_TOL2, GSL_SUCCESS);
442 TEST_SF(s, gsl_sf_conicalP_cyl_reg_e, (10, 1.0, 0.5, &r), 1.1674078819646475282e-09, TEST_TOL0, GSL_SUCCESS);
443 TEST_SF(s, gsl_sf_conicalP_cyl_reg_e, (20, 1.0, 0.5, &r), 7.066408031229072207e-24, TEST_TOL1, GSL_SUCCESS);
444 TEST_SF(s, gsl_sf_conicalP_cyl_reg_e, (30, 1.0, 0.5, &r), 2.6541973286862588488e-40, TEST_TOL1, GSL_SUCCESS);
445 TEST_SF(s, gsl_sf_conicalP_cyl_reg_e, (10, 1.0, 2.0, &r), 1.0736109751890863051e-09, TEST_TOL2, GSL_SUCCESS);
446 TEST_SF(s, gsl_sf_conicalP_cyl_reg_e, (20, 1.0, 2.0, &r), 6.760965304863386741e-24, TEST_TOL2, GSL_SUCCESS);
447 TEST_SF(s, gsl_sf_conicalP_cyl_reg_e, (30, 100.0, 100.0, &r), -4.268753482520651007e-63, TEST_TOL4, GSL_SUCCESS);
450 TEST_SF(s, gsl_sf_legendre_H3d_0_e, (1.0e-06, 1.0e-06, &r), 0.9999999999998333333 , TEST_TOL0, GSL_SUCCESS);
451 TEST_SF(s, gsl_sf_legendre_H3d_0_e, (1.0, 0.0, &r), 1.0 , TEST_TOL0, GSL_SUCCESS);
452 TEST_SF(s, gsl_sf_legendre_H3d_0_e, (1.0, 1.0, &r), 0.7160229153604338713 , TEST_TOL0, GSL_SUCCESS);
453 TEST_SF(s, gsl_sf_legendre_H3d_0_e, (1.0, 100.0, &r), -3.767437313149604566e-44 , TEST_TOL2, GSL_SUCCESS);
454 TEST_SF(s, gsl_sf_legendre_H3d_0_e, (1.0, 500.0, &r), -6.665351935878582205e-218, TEST_TOL2, GSL_SUCCESS);
455 TEST_SF(s, gsl_sf_legendre_H3d_0_e, (100.0, 1.0, &r), -0.004308757035378200029 , TEST_TOL0, GSL_SUCCESS);
456 TEST_SF(s, gsl_sf_legendre_H3d_0_e, (100.0, 10.0, &r), 7.508054627912986427e-07 , TEST_TOL0, GSL_SUCCESS);
457 TEST_SF(s, gsl_sf_legendre_H3d_0_e, (1000.0, 1.0, &r), 0.0007036067909088818319 , TEST_TOL0, GSL_SUCCESS);
458 TEST_SF(s, gsl_sf_legendre_H3d_0_e, (1.0e+08, 1.0, &r), 7.927485371429105968e-09 , TEST_TOL3, GSL_SUCCESS);
459 TEST_SF(s, gsl_sf_legendre_H3d_0_e, (1.0e+08, 100.0, &r), -3.627118904186918957e-52 , 32.0*TEST_SQRT_TOL0, GSL_SUCCESS);
461 TEST_SF(s, gsl_sf_legendre_H3d_1_e, (1.0e-06, 1.0e-06, &r), 3.333333333334222222e-07, TEST_TOL0, GSL_SUCCESS);
462 TEST_SF(s, gsl_sf_legendre_H3d_1_e, (1.0, 1.0e-10, &r), 4.714045207910316829e-11, TEST_TOL0, GSL_SUCCESS);
463 TEST_SF(s, gsl_sf_legendre_H3d_1_e, (1.0, 1.0, &r), 0.3397013994799344639, TEST_TOL0, GSL_SUCCESS);
464 TEST_SF(s, gsl_sf_legendre_H3d_1_e, (1.0, 100.0, &r), -7.200624449531811272e-44, TEST_TOL2, GSL_SUCCESS);
465 TEST_SF(s, gsl_sf_legendre_H3d_1_e, (1.0, 500.0, &r), 4.192260336821728677e-218, TEST_TOL2, GSL_SUCCESS);
466 TEST_SF(s, gsl_sf_legendre_H3d_1_e, (100.0, 0.01, &r), 0.30117664944267412324 , TEST_TOL1, GSL_SUCCESS);
467 TEST_SF(s, gsl_sf_legendre_H3d_1_e, (100.0, 1.0, &r), -0.007393833425336299309 , TEST_TOL0, GSL_SUCCESS);
468 TEST_SF(s, gsl_sf_legendre_H3d_1_e, (100.0, 10.0, &r), -5.031062029821254982e-07 , TEST_TOL0, GSL_SUCCESS);
469 TEST_SF(s, gsl_sf_legendre_H3d_1_e, (1000.0, 0.001, &r), 0.30116875865090396421 , TEST_TOL0, GSL_SUCCESS);
470 TEST_SF(s, gsl_sf_legendre_H3d_1_e, (1000.0, 1.0, &r), -0.0004776144516074971885 , TEST_TOL0, GSL_SUCCESS);
471 TEST_SF(s, gsl_sf_legendre_H3d_1_e, (1.0e+08, 1.0e-08, &r), 0.30116867893975679722 , TEST_TOL1, GSL_SUCCESS);
472 TEST_SF(s, gsl_sf_legendre_H3d_1_e, (1.0e+08, 1.0, &r), 3.0921097047369081582e-09, TEST_TOL4, GSL_SUCCESS);
473 TEST_SF(s, gsl_sf_legendre_H3d_1_e, (1.0e+08, 100.0, &r), -6.496142701296286936e-52 , 32.0*TEST_SQRT_TOL0, GSL_SUCCESS);
475 TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 1.0e-06, 1.0e-06, &r), 1.1544011544013627977e-32, TEST_TOL2, GSL_SUCCESS);
476 TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 1.0, 1.0e-10, &r), 2.0224912016958766992e-52, TEST_TOL2, GSL_SUCCESS);
477 TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 1.0, 1.0, &r), 0.011498635037491577728, TEST_TOL1, GSL_SUCCESS);
478 TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 1.0, 5.0, &r), 0.0020696945662545205776, TEST_TOL4, GSL_SUCCESS);
479 TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 1.0, 7.0, &r), -0.0017555303787488993676, TEST_TOL4, GSL_SUCCESS);
480 TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 1.0, 10.0, &r), 0.00008999979724504887101, TEST_TOL2, GSL_SUCCESS);
481 TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 1.0, 100.0, &r), -4.185397793298567945e-44, TEST_TOL2, GSL_SUCCESS);
482 TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 1.0, 500.0, &r), 1.4235113901091961263e-217, TEST_TOL3, GSL_SUCCESS);
483 TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 100.0, 0.001, &r), 9.642762597222417946e-10, TEST_TOL2, GSL_SUCCESS);
484 TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 100.0, 0.002, &r), 3.0821201254308036109e-08, TEST_TOL2, GSL_SUCCESS);
485 TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 100.0, 0.01, &r), 0.00009281069019005840532, TEST_TOL1, GSL_SUCCESS);
486 TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 100.0, 1.0, &r), -0.008043100696178624653, TEST_TOL2, GSL_SUCCESS);
487 TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 100.0, 10.0, &r), -3.927678432813974207e-07, TEST_TOL3, GSL_SUCCESS);
488 TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 1000.0, 0.001, &r), 0.00009256365284253254503, TEST_TOL1, GSL_SUCCESS);
489 TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 1000.0, 0.01, &r), -0.05553733815473079983, TEST_TOL0, GSL_SUCCESS);
490 TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 1.0e+08, 1.0e-08, &r), 0.00009256115861125841299, TEST_TOL2, GSL_SUCCESS);
491 TEST_SF(s, gsl_sf_legendre_H3d_e, (5, 1.0e+08, 100.0, &r), -6.496143209092860765e-52 , 128.0*TEST_SQRT_TOL0, GSL_SUCCESS);
495 gsl_sf_legendre_H3d_array(100, 1.0, 3.0, L);
496 TEST_SF_VAL(sa, L[0], +0.0, gsl_sf_legendre_H3d(0, 1.0, 3.0), 1.0e-12);
497 TEST_SF_VAL(sa, L[1], +0.0, gsl_sf_legendre_H3d(1, 1.0, 3.0), 1.0e-12);
498 TEST_SF_VAL(sa, L[10], +0.0, gsl_sf_legendre_H3d(10, 1.0, 3.0), 1.0e-12);
499 TEST_SF_VAL(sa, L[100], +0.0, gsl_sf_legendre_H3d(100, 1.0, 3.0), 1.0e-12);
500 gsl_test(sa, " gsl_sf_legendre_H3d_array(100, 1.0, 3.0)");
505 TEST_SF(s, gsl_sf_legendre_Q0_e, (-0.9999847412109375, &r), -5.8917472200477175158028143531855, TEST_TOL4, GSL_SUCCESS);
506 TEST_SF(s, gsl_sf_legendre_Q0_e, (-0.5, &r), -0.5493061443340548457, TEST_TOL0, GSL_SUCCESS);
507 TEST_SF(s, gsl_sf_legendre_Q0_e, (-1e-10, &r), -1.000000000000000000e-10, TEST_TOL0, GSL_SUCCESS);
508 TEST_SF(s, gsl_sf_legendre_Q0_e, (0.0, &r), 0.0, TEST_TOL0, GSL_SUCCESS);
509 TEST_SF(s, gsl_sf_legendre_Q0_e, (1e-10, &r), 1.000000000000000000e-10, TEST_TOL0, GSL_SUCCESS);
511 TEST_SF(s, gsl_sf_legendre_Q0_e, (0.9999847412109375, &r), 5.8917472200477175158028143531855, TEST_TOL4, GSL_SUCCESS);
513 TEST_SF(s, gsl_sf_legendre_Q0_e, ( 1.0000152587890625, &r), 5.8917548494422489138325509750429, TEST_TOL4, GSL_SUCCESS);
514 TEST_SF(s, gsl_sf_legendre_Q0_e, ( 1.5, &r), 0.8047189562170501873, TEST_TOL0, GSL_SUCCESS);
515 TEST_SF(s, gsl_sf_legendre_Q0_e, ( 9.99, &r), 0.1004364599660005447, TEST_TOL0, GSL_SUCCESS);
516 TEST_SF(s, gsl_sf_legendre_Q0_e, ( 10.0, &r), 0.1003353477310755806, TEST_TOL0, GSL_SUCCESS);
517 TEST_SF(s, gsl_sf_legendre_Q0_e, ( 10.01, &r), 0.1002344395571710243, TEST_TOL0, GSL_SUCCESS);
518 TEST_SF(s, gsl_sf_legendre_Q0_e, ( 100, &r), 0.010000333353334762015, TEST_TOL0, GSL_SUCCESS);
519 TEST_SF(s, gsl_sf_legendre_Q0_e, ( 1e10, &r), 1.000000000000000000e-10, TEST_TOL0, GSL_SUCCESS);
521 TEST_SF(s, gsl_sf_legendre_Q1_e, (-0.9999847412109375, &r), 4.8916573191196772369, TEST_TOL4, GSL_SUCCESS);
522 TEST_SF(s, gsl_sf_legendre_Q1_e, (-0.5, &r), -0.7253469278329725772, TEST_TOL0, GSL_SUCCESS);
523 TEST_SF(s, gsl_sf_legendre_Q1_e, (-0.01, &r), -0.9998999966664666524, TEST_TOL0, GSL_SUCCESS);
524 TEST_SF(s, gsl_sf_legendre_Q1_e, (-1e-10, &r), -0.999999999999999999, TEST_TOL0, GSL_SUCCESS);
525 TEST_SF(s, gsl_sf_legendre_Q1_e, (0.0, &r), -1.0, TEST_TOL0, GSL_SUCCESS);
526 TEST_SF(s, gsl_sf_legendre_Q1_e, (1e-10, &r), -0.999999999999999999, TEST_TOL0, GSL_SUCCESS);
527 TEST_SF(s, gsl_sf_legendre_Q1_e, (0.0001, &r), -0.9999999899999999667, TEST_TOL0, GSL_SUCCESS);
528 TEST_SF(s, gsl_sf_legendre_Q1_e, (0.01, &r), -0.9998999966664666524, TEST_TOL0, GSL_SUCCESS);
529 TEST_SF(s, gsl_sf_legendre_Q1_e, (0.5, &r), -0.7253469278329725772, TEST_TOL0, GSL_SUCCESS);
530 TEST_SF(s, gsl_sf_legendre_Q1_e, (0.9999847412109375, &r), 4.8916573191196772369, TEST_TOL4, GSL_SUCCESS);
531 TEST_SF(s, gsl_sf_legendre_Q1_e, (1.0000152587890625, &r), 4.8918447504867045145, TEST_TOL4, GSL_SUCCESS);
532 TEST_SF(s, gsl_sf_legendre_Q1_e, ( 1.5, &r), 0.20707843432557528095, TEST_TOL0, GSL_SUCCESS);
533 TEST_SF(s, gsl_sf_legendre_Q1_e, ( 9.99, &r), 3.360235060345441639e-3, TEST_TOL0, GSL_SUCCESS);
534 TEST_SF(s, gsl_sf_legendre_Q1_e, ( 10.0, &r), 3.353477310755806357e-3, TEST_TOL0, GSL_SUCCESS);
535 TEST_SF(s, gsl_sf_legendre_Q1_e, ( 10.01, &r), 3.346739967281953346e-3, TEST_TOL0, GSL_SUCCESS);
536 TEST_SF(s, gsl_sf_legendre_Q1_e, ( 100.0, &r), 3.333533347620158821e-5, TEST_TOL0, GSL_SUCCESS);
537 TEST_SF(s, gsl_sf_legendre_Q1_e, ( 1e10, &r), 3.333333333333333333e-21, TEST_TOL0, GSL_SUCCESS);
539 TEST_SF(s, gsl_sf_legendre_Ql_e, (10, -0.5, &r), -0.29165813966586752393, TEST_TOL0, GSL_SUCCESS);
540 TEST_SF(s, gsl_sf_legendre_Ql_e, (10, 0.5, &r), 0.29165813966586752393, TEST_TOL0, GSL_SUCCESS);
541 TEST_SF(s, gsl_sf_legendre_Ql_e, (10, 1.5, &r), 0.000014714232718207477406, TEST_TOL0, GSL_SUCCESS);
543 TEST_SF(s, gsl_sf_legendre_Ql_e, (100, -0.5, &r), -0.09492507395207282096, TEST_TOL1, GSL_SUCCESS);
544 TEST_SF(s, gsl_sf_legendre_Ql_e, (100, 0.5, &r), 0.09492507395207282096, TEST_TOL1, GSL_SUCCESS);
545 TEST_SF(s, gsl_sf_legendre_Ql_e, (100, 1.5, &r), 1.1628163435044121988e-43, TEST_TOL2, GSL_SUCCESS);
547 TEST_SF(s, gsl_sf_legendre_Ql_e, (1000, -0.5, &r), -0.030105074974005303500, TEST_TOL1, GSL_SUCCESS);
548 TEST_SF(s, gsl_sf_legendre_Ql_e, (1000, 0.5, &r), 0.030105074974005303500, TEST_TOL1, GSL_SUCCESS);
549 TEST_SF(s, gsl_sf_legendre_Ql_e, (1000, 1.1, &r), 1.0757258447825356443e-194, TEST_TOL3, GSL_SUCCESS);