mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
doc fmt
This commit is contained in:
fredrik
parent
5c26f5cc24
commit
c2168d5f9c
1 changed files with 25 additions and 50 deletions
|
|
@ -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)`.
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue