From c2168d5f9c2768f71e7c13ea1be94d7564d9d0f4 Mon Sep 17 00:00:00 2001 From: fredrik Date: Sun, 25 Jul 2021 14:33:50 +0200 Subject: [PATCH] doc fmt --- doc/source/arb_hypgeom.rst | 75 +++++++++++++------------------------- 1 file changed, 25 insertions(+), 50 deletions(-) diff --git a/doc/source/arb_hypgeom.rst b/doc/source/arb_hypgeom.rst index 5447c493..8e16dd37 100644 --- a/doc/source/arb_hypgeom.rst +++ b/doc/source/arb_hypgeom.rst @@ -148,8 +148,7 @@ Error functions and Fresnel integrals Computes the error function `\operatorname{erf}(z)`. .. function:: void _arb_hypgeom_erf_series(arb_ptr res, arb_srcptr z, slong zlen, slong len, slong prec) - -.. function:: void arb_hypgeom_erf_series(arb_poly_t res, const arb_poly_t z, slong len, slong prec) + void arb_hypgeom_erf_series(arb_poly_t res, const arb_poly_t z, slong len, slong prec) Computes the error function of the power series *z*, truncated to length *len*. @@ -161,8 +160,7 @@ Error functions and Fresnel integrals This function avoids catastrophic cancellation for large positive *z*. .. function:: void _arb_hypgeom_erfc_series(arb_ptr res, arb_srcptr z, slong zlen, slong len, slong prec) - -.. function:: void arb_hypgeom_erfc_series(arb_poly_t res, const arb_poly_t z, slong len, slong prec) + void arb_hypgeom_erfc_series(arb_poly_t res, const arb_poly_t z, slong len, slong prec) Computes the complementary error function of the power series *z*, truncated to length *len*. @@ -173,8 +171,7 @@ Error functions and Fresnel integrals `\operatorname{erfi}(z) = -i\operatorname{erf}(iz)`. .. function:: void _arb_hypgeom_erfi_series(arb_ptr res, arb_srcptr z, slong zlen, slong len, slong prec) - -.. function:: void arb_hypgeom_erfi_series(arb_poly_t res, const arb_poly_t z, slong len, slong prec) + void arb_hypgeom_erfi_series(arb_poly_t res, const arb_poly_t z, slong len, slong prec) Computes the imaginary error function of the power series *z*, truncated to length *len*. @@ -190,8 +187,7 @@ Error functions and Fresnel integrals `C(z)` is defined analogously. .. function:: void _arb_hypgeom_fresnel_series(arb_ptr res1, arb_ptr res2, arb_srcptr z, slong zlen, int normalized, slong len, slong prec) - -.. function:: void arb_hypgeom_fresnel_series(arb_poly_t res1, arb_poly_t res2, const arb_poly_t z, int normalized, slong len, slong prec) + void arb_hypgeom_fresnel_series(arb_poly_t res1, arb_poly_t res2, const arb_poly_t z, int normalized, slong len, slong prec) Sets *res1* to the Fresnel sine integral and *res2* to the Fresnel cosine integral of the power series *z*, truncated to length *len*. @@ -215,8 +211,7 @@ Incomplete gamma and beta functions interface for computing the exponential integral). .. function:: void _arb_hypgeom_gamma_upper_series(arb_ptr res, const arb_t s, arb_srcptr z, slong zlen, int regularized, slong n, slong prec) - -.. function:: void arb_hypgeom_gamma_upper_series(arb_poly_t res, const arb_t s, const arb_poly_t z, int regularized, slong n, slong prec) + void arb_hypgeom_gamma_upper_series(arb_poly_t res, const arb_t s, const arb_poly_t z, int regularized, slong n, slong prec) Sets *res* to an upper incomplete gamma function where *s* is a constant and *z* is a power series, truncated to length *n*. @@ -235,8 +230,7 @@ Incomplete gamma and beta functions gamma function `\gamma^{*}(s,z) = z^{-s} P(s,z)`. .. function:: void _arb_hypgeom_gamma_lower_series(arb_ptr res, const arb_t s, arb_srcptr z, slong zlen, int regularized, slong n, slong prec) - -.. function:: void arb_hypgeom_gamma_lower_series(arb_poly_t res, const arb_t s, const arb_poly_t z, int regularized, slong n, slong prec) + void arb_hypgeom_gamma_lower_series(arb_poly_t res, const arb_t s, const arb_poly_t z, int regularized, slong n, slong prec) Sets *res* to an lower incomplete gamma function where *s* is a constant and *z* is a power series, truncated to length *n*. @@ -251,8 +245,7 @@ Incomplete gamma and beta functions `I(a,b;z) = B(a,b;z) / B(a,b;1)`. .. function:: void _arb_hypgeom_beta_lower_series(arb_ptr res, const arb_t a, const arb_t b, arb_srcptr z, slong zlen, int regularized, slong n, slong prec) - -.. function:: void arb_hypgeom_beta_lower_series(arb_poly_t res, const arb_t a, const arb_t b, const arb_poly_t z, int regularized, slong n, slong prec) + void arb_hypgeom_beta_lower_series(arb_poly_t res, const arb_t a, const arb_t b, const arb_poly_t z, int regularized, slong n, slong prec) Sets *res* to the lower incomplete beta function `B(a,b;z)` (optionally the regularized version `I(a,b;z)`) where *a* and *b* are constants @@ -272,8 +265,7 @@ Exponential and trigonometric integrals Computes the exponential integral `\operatorname{Ei}(z)`. .. function:: void _arb_hypgeom_ei_series(arb_ptr res, arb_srcptr z, slong zlen, slong len, slong prec) - -.. function:: void arb_hypgeom_ei_series(arb_poly_t res, const arb_poly_t z, slong len, slong prec) + void arb_hypgeom_ei_series(arb_poly_t res, const arb_poly_t z, slong len, slong prec) Computes the exponential integral of the power series *z*, truncated to length *len*. @@ -283,8 +275,7 @@ Exponential and trigonometric integrals Computes the sine integral `\operatorname{Si}(z)`. .. function:: void _arb_hypgeom_si_series(arb_ptr res, arb_srcptr z, slong zlen, slong len, slong prec) - -.. function:: void arb_hypgeom_si_series(arb_poly_t res, const arb_poly_t z, slong len, slong prec) + void arb_hypgeom_si_series(arb_poly_t res, const arb_poly_t z, slong len, slong prec) Computes the sine integral of the power series *z*, truncated to length *len*. @@ -295,8 +286,7 @@ Exponential and trigonometric integrals The result is indeterminate if `z < 0` since the value of the function would be complex. .. function:: void _arb_hypgeom_ci_series(arb_ptr res, arb_srcptr z, slong zlen, slong len, slong prec) - -.. function:: void arb_hypgeom_ci_series(arb_poly_t res, const arb_poly_t z, slong len, slong prec) + void arb_hypgeom_ci_series(arb_poly_t res, const arb_poly_t z, slong len, slong prec) Computes the cosine integral of the power series *z*, truncated to length *len*. @@ -306,8 +296,7 @@ Exponential and trigonometric integrals Computes the hyperbolic sine integral `\operatorname{Shi}(z) = -i \operatorname{Si}(iz)`. .. function:: void _arb_hypgeom_shi_series(arb_ptr res, arb_srcptr z, slong zlen, slong len, slong prec) - -.. function:: void arb_hypgeom_shi_series(arb_poly_t res, const arb_poly_t z, slong len, slong prec) + void arb_hypgeom_shi_series(arb_poly_t res, const arb_poly_t z, slong len, slong prec) Computes the hyperbolic sine integral of the power series *z*, truncated to length *len*. @@ -318,8 +307,7 @@ Exponential and trigonometric integrals The result is indeterminate if `z < 0` since the value of the function would be complex. .. function:: void _arb_hypgeom_chi_series(arb_ptr res, arb_srcptr z, slong zlen, slong len, slong prec) - -.. function:: void arb_hypgeom_chi_series(arb_poly_t res, const arb_poly_t z, slong len, slong prec) + void arb_hypgeom_chi_series(arb_poly_t res, const arb_poly_t z, slong len, slong prec) Computes the hyperbolic cosine integral of the power series *z*, truncated to length *len*. @@ -335,8 +323,7 @@ Exponential and trigonometric integrals The result is indeterminate if `z < 0` since the value of the function would be complex. .. function:: void _arb_hypgeom_li_series(arb_ptr res, arb_srcptr z, slong zlen, int offset, slong len, slong prec) - -.. function:: void arb_hypgeom_li_series(arb_poly_t res, const arb_poly_t z, int offset, slong len, slong prec) + void arb_hypgeom_li_series(arb_poly_t res, const arb_poly_t z, int offset, slong len, slong prec) Computes the logarithmic integral (optionally the offset version) of the power series *z*, truncated to length *len*. @@ -395,8 +382,7 @@ Airy functions the output with :func:`_arb_poly_derivative`. .. function:: void _arb_hypgeom_airy_series(arb_ptr ai, arb_ptr ai_prime, arb_ptr bi, arb_ptr bi_prime, arb_srcptr z, slong zlen, slong len, slong prec) - -.. function:: void arb_hypgeom_airy_series(arb_poly_t ai, arb_poly_t ai_prime, arb_poly_t bi, arb_poly_t bi_prime, const arb_poly_t z, slong len, slong prec) + void arb_hypgeom_airy_series(arb_poly_t ai, arb_poly_t ai_prime, arb_poly_t bi, arb_poly_t bi_prime, const arb_poly_t z, slong len, slong prec) Computes the Airy functions evaluated at the power series *z*, truncated to length *len*. As with the other Airy methods, any of the @@ -429,8 +415,7 @@ Coulomb wave functions Either of the outputs can be *NULL*. .. function:: void _arb_hypgeom_coulomb_series(arb_ptr F, arb_ptr G, const arb_t l, const arb_t eta, arb_srcptr z, slong zlen, slong len, slong prec) - -.. function:: void arb_hypgeom_coulomb_series(arb_poly_t F, arb_poly_t G, const arb_t l, const arb_t eta, const arb_poly_t z, slong len, slong prec) + void arb_hypgeom_coulomb_series(arb_poly_t F, arb_poly_t G, const arb_t l, const arb_t eta, const arb_poly_t z, slong len, slong prec) Computes the Coulomb wave functions evaluated at the power series *z*, truncated to length *len*. Either of the outputs can be *NULL*. @@ -439,23 +424,17 @@ Orthogonal polynomials and functions ------------------------------------------------------------------------------- .. function:: void arb_hypgeom_chebyshev_t(arb_t res, const arb_t nu, const arb_t z, slong prec) - -.. function:: void arb_hypgeom_chebyshev_u(arb_t res, const arb_t nu, const arb_t z, slong prec) - -.. function:: void arb_hypgeom_jacobi_p(arb_t res, const arb_t n, const arb_t a, const arb_t b, const arb_t z, slong prec) - -.. function:: void arb_hypgeom_gegenbauer_c(arb_t res, const arb_t n, const arb_t m, const arb_t z, slong prec) - -.. function:: void arb_hypgeom_laguerre_l(arb_t res, const arb_t n, const arb_t m, const arb_t z, slong prec) - -.. function:: void arb_hypgeom_hermite_h(arb_t res, const arb_t nu, const arb_t z, slong prec) + void arb_hypgeom_chebyshev_u(arb_t res, const arb_t nu, const arb_t z, slong prec) + void arb_hypgeom_jacobi_p(arb_t res, const arb_t n, const arb_t a, const arb_t b, const arb_t z, slong prec) + void arb_hypgeom_gegenbauer_c(arb_t res, const arb_t n, const arb_t m, const arb_t z, slong prec) + void arb_hypgeom_laguerre_l(arb_t res, const arb_t n, const arb_t m, const arb_t z, slong prec) + void arb_hypgeom_hermite_h(arb_t res, const arb_t nu, const arb_t z, slong prec) Computes Chebyshev, Jacobi, Gegenbauer, Laguerre or Hermite polynomials, or their extensions to non-integer orders. .. function:: void arb_hypgeom_legendre_p(arb_t res, const arb_t n, const arb_t m, const arb_t z, int type, slong prec) - -.. function:: void arb_hypgeom_legendre_q(arb_t res, const arb_t n, const arb_t m, const arb_t z, int type, slong prec) + void arb_hypgeom_legendre_q(arb_t res, const arb_t n, const arb_t m, const arb_t z, int type, slong prec) Computes Legendre functions of the first and second kind. See :func:`acb_hypgeom_legendre_p` and :func:`acb_hypgeom_legendre_q` @@ -470,14 +449,10 @@ Orthogonal polynomials and functions internally to bound the propagated error for Legendre polynomials. .. function:: void arb_hypgeom_legendre_p_ui_zero(arb_t res, arb_t res_prime, ulong n, const arb_t x, slong K, slong prec) - -.. function:: void arb_hypgeom_legendre_p_ui_one(arb_t res, arb_t res_prime, ulong n, const arb_t x, slong K, slong prec) - -.. function:: void arb_hypgeom_legendre_p_ui_asymp(arb_t res, arb_t res_prime, ulong n, const arb_t x, slong K, slong prec) - -.. function:: void arb_hypgeom_legendre_p_rec(arb_t res, arb_t res_prime, ulong n, const arb_t x, slong prec) - -.. function:: void arb_hypgeom_legendre_p_ui(arb_t res, arb_t res_prime, ulong n, const arb_t x, slong prec) + void arb_hypgeom_legendre_p_ui_one(arb_t res, arb_t res_prime, ulong n, const arb_t x, slong K, slong prec) + void arb_hypgeom_legendre_p_ui_asymp(arb_t res, arb_t res_prime, ulong n, const arb_t x, slong K, slong prec) + void arb_hypgeom_legendre_p_rec(arb_t res, arb_t res_prime, ulong n, const arb_t x, slong prec) + void arb_hypgeom_legendre_p_ui(arb_t res, arb_t res_prime, ulong n, const arb_t x, slong prec) Evaluates the ordinary Legendre polynomial `P_n(x)`. If *res_prime* is non-NULL, simultaneously evaluates the derivative `P'_n(x)`.