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avoid another square root, and fix formula in the documentation

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Fredrik Johansson 2016-03-19 14:39:05 +01:00
parent 8dfba32d8c
commit 2ba3e36dbd
2 changed files with 3 additions and 4 deletions
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5
acb_hypgeom/erf.c
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@ -142,10 +142,9 @@ acb_hypgeom_erf_asymp(acb_t res, const acb_t z, int complementary, slong prec, s
acb_exp(t, t, prec2); acb_exp(t, t, prec2);
acb_mul(u, u, t, prec2); acb_mul(u, u, t, prec2);
acb_const_pi(t, prec2); arb_const_sqrt_pi(acb_realref(t), prec2);
acb_sqrt(t, t, prec2); arb_zero(acb_imagref(t));
acb_mul(t, t, z, prec2); acb_mul(t, t, z, prec2);
acb_div(u, u, t, prec2); acb_div(u, u, t, prec2);
/* branch cut term: -1 or 1 */ /* branch cut term: -1 or 1 */

2
doc/source/acb_hypgeom.rst
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@ -251,7 +251,7 @@ Error functions and Fresnel integrals
\operatorname{erf}(z) &= \frac{z}{\sqrt{z^2}} \operatorname{erf}(z) &= \frac{z}{\sqrt{z^2}}
\left(1 - \frac{e^{-z^2}}{\sqrt{\pi}} \left(1 - \frac{e^{-z^2}}{\sqrt{\pi}}
U(\tfrac{1}{2}, \tfrac{1}{2}, z^2)\right) = U(\tfrac{1}{2}, \tfrac{1}{2}, z^2)\right) =
\frac{z}{\sqrt{z^2}} - \frac{z e^{-z^2}}{\sqrt{\pi}} \frac{z}{\sqrt{z^2}} - \frac{e^{-z^2}}{z \sqrt{\pi}}
U^{*}(\tfrac{1}{2}, \tfrac{1}{2}, z^2). U^{*}(\tfrac{1}{2}, \tfrac{1}{2}, z^2).
The *asymp* version takes a second precision to use for the *U* term. The *asymp* version takes a second precision to use for the *U* term.