Hypergeometric functions

Common hypergeometric series

For convenience, most of the hypergeometric series of low order are provided as standalone functions. They can equivalently be evaluated using hyper(). As will be demonstrated further in the individual docstrings, all the following functions implement analytic continuations and/or asymptotic expansions with respect to the argument , thereby permitting evaluation anywhere in the complex plane. Functions of higher degree can be computed via hyper(), but generally only in rapidly convergent instances.

hyp0f1()

hyp1f1()

hyp1f2()

hyp2f0()

hyp2f1()

hyp2f2()

hyp2f3()

Generalized hypergeometric functions

hyper()

hypercomb()

Confluent U and Whittaker functions

hyperu()

whitm()

whitw()

Meijer G-function

meijerg()

Appell hypergeometric function of two variables

appellf1()