void acb_hypgeom_bessel_jy(acb_t res1, acb_t res2, const acb_t nu, const acb_t z, slong prec) { acb_t jnu, t, u, v; acb_init(jnu); acb_init(t); acb_init(u); acb_init(v); acb_hypgeom_bessel_j(jnu, nu, z, prec); if (acb_is_int(nu)) { int is_real = acb_is_real(nu) && acb_is_real(z) && arb_is_positive(acb_realref(z)); acb_mul_onei(t, z); acb_hypgeom_bessel_k(t, nu, t, prec); acb_onei(u); acb_pow(u, u, nu, prec); acb_mul(t, t, u, prec); acb_const_pi(u, prec); acb_div(t, t, u, prec); acb_mul_2exp_si(t, t, 1); acb_neg(t, t); phase(v, acb_realref(z), acb_imagref(z)); acb_mul(u, jnu, v, prec); acb_mul_onei(u, u); acb_sub(res2, t, u, prec); if (is_real) arb_zero(acb_imagref(res2)); } else { acb_sin_cos_pi(t, u, nu, prec); acb_mul(v, jnu, u, prec); acb_neg(u, nu); acb_hypgeom_bessel_j(u, u, z, prec); acb_sub(v, v, u, prec); acb_div(res2, v, t, prec); } if (res1 != NULL) acb_set(res1, jnu); acb_clear(jnu); acb_clear(t); acb_clear(u); acb_clear(v); }
void arb_hypgeom_bessel_j(arb_t res, const arb_t nu, const arb_t z, slong prec) { acb_t t, u; acb_init(t); acb_init(u); arb_set(acb_realref(t), nu); arb_set(acb_realref(u), z); acb_hypgeom_bessel_j(t, t, u, prec); if (acb_is_finite(t) && acb_is_real(t)) arb_swap(res, acb_realref(t)); else arb_indeterminate(res); acb_clear(t); acb_clear(u); }
int main() { long iter; flint_rand_t state; printf("bessel_j...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 2000; iter++) { acb_t nu0, nu1, nu2, z, w0, w1, w2, t, u; long prec0, prec1, prec2; acb_init(nu0); acb_init(nu1); acb_init(nu2); acb_init(z); acb_init(w0); acb_init(w1); acb_init(w2); acb_init(t); acb_init(u); prec0 = 2 + n_randint(state, 1000); prec1 = 2 + n_randint(state, 1000); prec2 = 2 + n_randint(state, 1000); acb_randtest_param(nu0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(z, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(w0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(w1, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(w2, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_sub_ui(nu1, nu0, 1, prec0); acb_sub_ui(nu2, nu0, 2, prec0); switch (n_randint(state, 3)) { case 0: acb_hypgeom_bessel_j_asymp(w0, nu0, z, prec0); break; case 1: acb_hypgeom_bessel_j_0f1(w0, nu0, z, prec0); break; default: acb_hypgeom_bessel_j(w0, nu0, z, prec0); } switch (n_randint(state, 3)) { case 0: acb_hypgeom_bessel_j_asymp(w1, nu0, z, prec1); break; case 1: acb_hypgeom_bessel_j_0f1(w1, nu0, z, prec1); break; default: acb_hypgeom_bessel_j(w1, nu0, z, prec1); } if (!acb_overlaps(w0, w1)) { printf("FAIL: consistency\n\n"); printf("nu = "); acb_printd(nu0, 30); printf("\n\n"); printf("z = "); acb_printd(z, 30); printf("\n\n"); printf("w0 = "); acb_printd(w0, 30); printf("\n\n"); printf("w1 = "); acb_printd(w1, 30); printf("\n\n"); abort(); } switch (n_randint(state, 3)) { case 0: acb_hypgeom_bessel_j_asymp(w1, nu1, z, prec1); break; case 1: acb_hypgeom_bessel_j_0f1(w1, nu1, z, prec1); break; default: acb_hypgeom_bessel_j(w1, nu1, z, prec1); } switch (n_randint(state, 3)) { case 0: acb_hypgeom_bessel_j_asymp(w2, nu2, z, prec2); break; case 1: acb_hypgeom_bessel_j_0f1(w2, nu2, z, prec2); break; default: acb_hypgeom_bessel_j(w2, nu2, z, prec2); } acb_mul(t, w1, nu1, prec0); acb_mul_2exp_si(t, t, 1); acb_submul(t, w2, z, prec0); acb_submul(t, w0, z, prec0); if (!acb_contains_zero(t)) { printf("FAIL: contiguous relation\n\n"); printf("nu = "); acb_printd(nu0, 30); printf("\n\n"); printf("z = "); acb_printd(z, 30); printf("\n\n"); printf("w0 = "); acb_printd(w0, 30); printf("\n\n"); printf("w1 = "); acb_printd(w1, 30); printf("\n\n"); printf("w2 = "); acb_printd(w2, 30); printf("\n\n"); printf("t = "); acb_printd(t, 30); printf("\n\n"); abort(); } acb_neg(t, nu0); switch (n_randint(state, 3)) { case 0: acb_hypgeom_bessel_j_asymp(w2, t, z, prec2); break; case 1: acb_hypgeom_bessel_j_0f1(w2, t, z, prec2); break; default: acb_hypgeom_bessel_j(w2, t, z, prec2); } acb_mul(w1, w1, w2, prec2); acb_neg(t, nu1); switch (n_randint(state, 3)) { case 0: acb_hypgeom_bessel_j_asymp(w2, t, z, prec2); break; case 1: acb_hypgeom_bessel_j_0f1(w2, t, z, prec2); break; default: acb_hypgeom_bessel_j(w2, t, z, prec2); } acb_mul(w0, w0, w2, prec2); acb_add(w0, w0, w1, prec2); acb_sin_pi(t, nu0, prec2); acb_const_pi(u, prec2); acb_mul(u, u, z, prec2); acb_div(t, t, u, prec2); acb_mul_2exp_si(t, t, 1); if (!acb_overlaps(w0, t)) { printf("FAIL: wronskian\n\n"); printf("nu = "); acb_printd(nu0, 30); printf("\n\n"); printf("z = "); acb_printd(z, 30); printf("\n\n"); printf("w0 = "); acb_printd(w0, 30); printf("\n\n"); printf("t = "); acb_printd(t, 30); printf("\n\n"); abort(); } acb_clear(nu0); acb_clear(nu1); acb_clear(nu2); acb_clear(z); acb_clear(w0); acb_clear(w1); acb_clear(w2); acb_clear(t); acb_clear(u); } flint_randclear(state); flint_cleanup(); printf("PASS\n"); return EXIT_SUCCESS; }