gr_series_gamma, gr_series_rgamma, gr_series_lgamma, gr_series_digamma, gr_series_erf, gr_series_erfc, gr_series_erfi, gr_series_exp_integral_ei, gr_series_cos_integral, gr_series_cosh_integral, gr_series_sin_integral, gr_series_sinh_integral, gr_series_fresnel, gr_series_fresnel_s, gr_series_fresnel_c, gr_series_bessel_j, gr_series_airy, gr_series_airy_ai, gr_series_airy_ai_prime, gr_series_airy_bi, gr_series_airy_bi_prime, gr_series_log_integral, gr_series_gamma_upper, gr_series_gamma_lower, gr_series_beta_lower, gr_series_polylog, gr_series_hurwitz_zeta, gr_series_dirichlet_l, gr_series_dirichlet_hardy_theta, gr_series_dirichlet_hardy_z, gr_series_jacobi_theta, gr_series_jacobi_theta_1, gr_series_jacobi_theta_2, gr_series_jacobi_theta_3, gr_series_jacobi_theta_4, gr_series_agm1, gr_series_elliptic_k, gr_series_weierstrass_p, gr_series_hypgeom_pfq
#include <flint/gr_series.h>int gr_series_gamma(gr_series_t res, const gr_series_t x, gr_ctx_t ctx)sourceint gr_series_rgamma(gr_series_t res, const gr_series_t x, gr_ctx_t ctx)sourceint gr_series_lgamma(gr_series_t res, const gr_series_t x, gr_ctx_t ctx)sourceint gr_series_digamma(gr_series_t res, const gr_series_t x, gr_ctx_t ctx)sourceint gr_series_erf(gr_series_t res, const gr_series_t x, gr_ctx_t ctx)sourceint gr_series_erfc(gr_series_t res, const gr_series_t x, gr_ctx_t ctx)sourceint gr_series_erfi(gr_series_t res, const gr_series_t x, gr_ctx_t ctx)sourceint gr_series_exp_integral_ei(gr_series_t res, const gr_series_t x, gr_ctx_t ctx)sourceint gr_series_cos_integral(gr_series_t res, const gr_series_t x, gr_ctx_t ctx)sourceint gr_series_cosh_integral(gr_series_t res, const gr_series_t x, gr_ctx_t ctx)sourceint gr_series_sin_integral(gr_series_t res, const gr_series_t x, gr_ctx_t ctx)sourceint gr_series_sinh_integral(gr_series_t res, const gr_series_t x, gr_ctx_t ctx)sourceint gr_series_fresnel(gr_series_t res1, gr_series_t res2, const gr_series_t x, int normalized, gr_ctx_t ctx)sourceint gr_series_fresnel_s(gr_series_t res, const gr_series_t x, int normalized, gr_ctx_t ctx)sourceint gr_series_fresnel_c(gr_series_t res, const gr_series_t x, int normalized, gr_ctx_t ctx)sourceint gr_series_bessel_j(gr_series_t res, const gr_srcptr nu, const gr_series_t z, gr_ctx_t ctx)sourceint gr_series_airy(gr_series_t res1, gr_series_t res2, gr_series_t res3, gr_series_t res4, const gr_series_t x, gr_ctx_t ctx)sourceint gr_series_airy_ai(gr_series_t res, const gr_series_t x, gr_ctx_t ctx)sourceint gr_series_airy_ai_prime(gr_series_t res, const gr_series_t x, gr_ctx_t ctx)sourceint gr_series_airy_bi(gr_series_t res, const gr_series_t x, gr_ctx_t ctx)sourceint gr_series_airy_bi_prime(gr_series_t res, const gr_series_t x, gr_ctx_t ctx)sourceint gr_series_log_integral(gr_series_t res, const gr_series_t x, int offset, gr_ctx_t ctx)sourceint gr_series_gamma_upper(gr_series_t res, const gr_series_t s, const gr_series_t x, int regularized, gr_ctx_t ctx)sourceint gr_series_gamma_lower(gr_series_t res, const gr_series_t s, const gr_series_t x, int regularized, gr_ctx_t ctx)sourceint gr_series_beta_lower(gr_series_t res, const gr_series_t a, const gr_series_t b, const gr_series_t x, int regularized, gr_ctx_t ctx)sourceint gr_series_polylog(gr_series_t res, const gr_series_t s, const gr_series_t z, gr_ctx_t ctx)sourceint gr_series_hurwitz_zeta(gr_series_t res, const gr_series_t s, const gr_series_t z, gr_ctx_t ctx)sourceint gr_series_dirichlet_l(gr_series_t res, const dirichlet_group_t G, const dirichlet_char_t chi, const gr_series_t x, gr_ctx_t ctx)sourceint gr_series_dirichlet_hardy_theta(gr_series_t res, const dirichlet_group_t G, const dirichlet_char_t chi, const gr_series_t x, gr_ctx_t ctx)sourceint gr_series_dirichlet_hardy_z(gr_series_t res, const dirichlet_group_t G, const dirichlet_char_t chi, const gr_series_t x, gr_ctx_t ctx)sourceint gr_series_jacobi_theta(gr_series_t res1, gr_series_t res2, gr_series_t res3, gr_series_t res4, const gr_series_t x, const gr_series_t tau, gr_ctx_t ctx)sourceint gr_series_jacobi_theta_1(gr_series_t res, const gr_series_t x, const gr_series_t tau, gr_ctx_t ctx)sourceint gr_series_jacobi_theta_2(gr_series_t res, const gr_series_t x, const gr_series_t tau, gr_ctx_t ctx)sourceint gr_series_jacobi_theta_3(gr_series_t res, const gr_series_t x, const gr_series_t tau, gr_ctx_t ctx)sourceint gr_series_jacobi_theta_4(gr_series_t res, const gr_series_t x, const gr_series_t tau, gr_ctx_t ctx)sourceint gr_series_agm1(gr_series_t res, const gr_series_t x, gr_ctx_t ctx)sourceint gr_series_elliptic_k(gr_series_t res, const gr_series_t x, gr_ctx_t ctx)sourceint gr_series_weierstrass_p(gr_series_t res, const gr_series_t x, const gr_series_t tau, gr_ctx_t ctx)sourceint gr_series_hypgeom_pfq(gr_series_t res, const gr_series_vec_t a, const gr_series_vec_t b, const gr_series_t x, int regularized, gr_ctx_t ctx)sourceSpecial functions of power series. These are currently implemented only over the base rings arb and acb, through the series functions of arb_hypgeom, acb_hypgeom, acb_dirichlet, acb_elliptic and acb_modular (for example arb_hypgeom_gamma_series), and return GR_UNABLE for other base rings. The flags normalized, offset and regularized have the meanings of the corresponding arb_hypgeom functions. For the functions of two or more series arguments, all arguments except one must currently be constant series.
The FLINT team, “gr_series_gamma, gr_series_rgamma, gr_series_lgamma, gr_series_digamma, gr_series_erf, gr_series_erfc, gr_series_erfi, gr_series_exp_integral_ei, gr_series_cos_integral, gr_series_cosh_integral, gr_series_sin_integral, gr_series_sinh_integral, gr_series_fresnel, gr_series_fresnel_s, gr_series_fresnel_c, gr_series_bessel_j, gr_series_airy, gr_series_airy_ai, gr_series_airy_ai_prime, gr_series_airy_bi, gr_series_airy_bi_prime, gr_series_log_integral, gr_series_gamma_upper, gr_series_gamma_lower, gr_series_beta_lower, gr_series_polylog, gr_series_hurwitz_zeta, gr_series_dirichlet_l, gr_series_dirichlet_hardy_theta, gr_series_dirichlet_hardy_z, gr_series_jacobi_theta, gr_series_jacobi_theta_1, gr_series_jacobi_theta_2, gr_series_jacobi_theta_3, gr_series_jacobi_theta_4, gr_series_agm1, gr_series_elliptic_k, gr_series_weierstrass_p, gr_series_hypgeom_pfq (gr_series.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/gr_series/gr_series_gamma.html (generated 2026-10-20).
@misc{flint-doc-gr-series-gr-series-gamma,
author = {{The FLINT team}},
title = {{gr\_series\_gamma, gr\_series\_rgamma, gr\_series\_lgamma, gr\_series\_digamma, gr\_series\_erf, gr\_series\_erfc, gr\_series\_erfi, gr\_series\_exp\_integral\_ei, gr\_series\_cos\_integral, gr\_series\_cosh\_integral, gr\_series\_sin\_integral, gr\_series\_sinh\_integral, gr\_series\_fresnel, gr\_series\_fresnel\_s, gr\_series\_fresnel\_c, gr\_series\_bessel\_j, gr\_series\_airy, gr\_series\_airy\_ai, gr\_series\_airy\_ai\_prime, gr\_series\_airy\_bi, gr\_series\_airy\_bi\_prime, gr\_series\_log\_integral, gr\_series\_gamma\_upper, gr\_series\_gamma\_lower, gr\_series\_beta\_lower, gr\_series\_polylog, gr\_series\_hurwitz\_zeta, gr\_series\_dirichlet\_l, gr\_series\_dirichlet\_hardy\_theta, gr\_series\_dirichlet\_hardy\_z, gr\_series\_jacobi\_theta, gr\_series\_jacobi\_theta\_1, gr\_series\_jacobi\_theta\_2, gr\_series\_jacobi\_theta\_3, gr\_series\_jacobi\_theta\_4, gr\_series\_agm1, gr\_series\_elliptic\_k, gr\_series\_weierstrass\_p, gr\_series\_hypgeom\_pfq (gr\_series.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/gr_series/gr_series_gamma.html},
note = {Generated 2026-10-20}
}