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@@ -222,7 +222,7 @@ Confluent hypergeometric functions
Bessel-*I * function is used in the right half-plane, to avoid loss
of accuracy due to evaluating the square root on the branch cut.
The error function
Error functions and Fresnel integrals
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.. function :: void acb_hypgeom_erf_propagated_error(mag_t re, mag_t im, const acb_t z)
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@@ -299,6 +299,16 @@ The error function
Computes the imaginary error function of the power series *z *,
truncated to length *len *.
.. function :: void acb_hypgeom_fresnel(acb_t res1, acb_t res2, const acb_t z, int normalized, slong prec)
Sets *res1 * to the Fresnel sine integral `S(z) ` and *res2 * to
the Fresnel cosine integral `C(z) `. Optionally, just a single function
can be computed by passing *NULL * as the other output variable.
The definition `S(z) = \int_0^z \sin(t^2) dt ` is used if *normalized * is 0,
and `S(z) = \int_0^z \sin(\tfrac{1}{2} \pi t^2) dt ` is used if
*normalized * is 1 (the latter is the Abramowitz & Stegun convention).
`C(z) ` is defined analogously.
Bessel functions
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