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wrap bessel functions for arb_hypgeom

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This commit is contained in:
Fredrik Johansson 2016-09-05 21:32:19 +02:00
parent 5a3778befc
commit 5468d7d31b
3 changed files with 119 additions and 0 deletions
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6
arb_hypgeom.h
View file

@ -68,6 +68,12 @@ void arb_hypgeom_li(arb_t res, const arb_t z, int offset, slong prec);
void _arb_hypgeom_li_series(arb_ptr g, arb_srcptr h, slong hlen, int offset, slong len, slong prec);
void arb_hypgeom_li_series(arb_poly_t g, const arb_poly_t h, int offset, slong len, slong prec);
void arb_hypgeom_bessel_j(arb_t res, const arb_t nu, const arb_t z, slong prec);
void arb_hypgeom_bessel_y(arb_t res, const arb_t nu, const arb_t z, slong prec);
void arb_hypgeom_bessel_jy(arb_t res1, arb_t res2, const arb_t nu, const arb_t z, slong prec);
void arb_hypgeom_bessel_i(arb_t res, const arb_t nu, const arb_t z, slong prec);
void arb_hypgeom_bessel_k(arb_t res, const arb_t nu, const arb_t z, slong prec);
void arb_hypgeom_airy(arb_t ai, arb_t aip, arb_t bi, arb_t bip, const arb_t z, slong prec);
void arb_hypgeom_airy_jet(arb_ptr ai, arb_ptr bi, const arb_t z, slong len, slong prec);
void arb_hypgeom_airy_series(arb_poly_t ai, arb_poly_t ai_prime,

88
arb_hypgeom/wrappers.c
View file

@ -301,3 +301,91 @@ arb_hypgeom_pfq(arb_t res, arb_srcptr a, slong p, arb_srcptr b, slong q, const a
_acb_vec_clear(t, p + q + 1);
}
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);
}
void
arb_hypgeom_bessel_y(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_y(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);
}
void
arb_hypgeom_bessel_jy(arb_t res1, arb_t res2, 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_jy(t, u, t, u, prec);
if (acb_is_finite(t) && acb_is_real(t))
arb_swap(res1, acb_realref(t));
else
arb_indeterminate(res1);
if (acb_is_finite(u) && acb_is_real(u))
arb_swap(res2, acb_realref(u));
else
arb_indeterminate(res2);
acb_clear(t);
acb_clear(u);
}
void
arb_hypgeom_bessel_i(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_i(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);
}
void
arb_hypgeom_bessel_k(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_k(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);
}

25
doc/source/arb_hypgeom.rst
View file

@ -191,6 +191,31 @@ Exponential and trigonometric integrals
Computes the logarithmic integral (optionally the offset version)
of the power series *z*, truncated to length *len*.
Bessel functions
-------------------------------------------------------------------------------
.. function:: void arb_hypgeom_bessel_j(arb_t res, const arb_t nu, const arb_t z, slong prec)
Computes the Bessel function of the first kind `J_{\nu}(z)`.
.. function:: void arb_hypgeom_bessel_y(arb_t res, const arb_t nu, const arb_t z, slong prec)
Computes the Bessel function of the second kind `Y_{\nu}(z)`.
.. function:: void arb_hypgeom_bessel_jy(arb_t res1, arb_t res2, const arb_t nu, const arb_t z, slong prec)
Sets *res1* to `J_{\nu}(z)` and *res2* to `Y_{\nu}(z)`, computed
simultaneously.
.. function:: void arb_hypgeom_bessel_i(arb_t res, const arb_t nu, const arb_t z, slong prec)
Computes the modified Bessel function of the first kind
`I_{\nu}(z) = z^{\nu} (iz)^{-\nu} J_{\nu}(iz)`.
.. function:: void arb_hypgeom_bessel_k(arb_t res, const arb_t nu, const arb_t z, slong prec)
Computes the modified Bessel function of the second kind `K_{\nu}(z)`.
Airy functions
-------------------------------------------------------------------------------