# scipy.special.hyp2f1¶

scipy.special.hyp2f1(a, b, c, z) = <ufunc 'hyp2f1'>

Gauss hypergeometric function 2F1(a, b; c; z)

Parameters: a, b, c : array_like Arguments, should be real-valued. z : array_like Argument, real or complex. hyp2f1 : scalar or ndarray The values of the gaussian hypergeometric function.

hyp0f1
confluent hypergeometric limit function.
hyp1f1
Kummer’s (confluent hypergeometric) function.

Notes

This function is defined for $$|z| < 1$$ as

$\mathrm{hyp2f1}(a, b, c, z) = \sum_{n=0}^\infty \frac{(a)_n (b)_n}{(c)_n}\frac{z^n}{n!},$

and defined on the rest of the complex z-plane by analytic continuation. Here $$(\cdot)_n$$ is the Pochhammer symbol; see poch. When $$n$$ is an integer the result is a polynomial of degree $$n$$.

The implementation for complex values of z is described in [1].

References

 [1] (1, 2) Zhang and J.M. Jin, “Computation of Special Functions”, Wiley 1996
 [2] Cephes Mathematical Functions Library, http://www.netlib.org/cephes/index.html
 [3] NIST Digital Library of Mathematical Functions http://dlmf.nist.gov/

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