Generalized hypergeometric function

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a generalized hypergeometric series is a <a href="/facts/Power_series/vYh6sTps">power series</a> in which the ratio of successive <a href="/facts/Coefficient/5Hwq2Wuq">coefficients</a> indexed by n is a <a href="/facts/Rational_function/2nJGu0Ko">rational function</a> of n. The series, if convergent, defines a generalized hypergeometric function, which may then be defined over a wider domain of the argument by <a href="/facts/Analytic_continuation/aBCuEgvt">analytic continuation</a>. The generalized hypergeometric series is sometimes just called the hypergeometric series, though this term also sometimes just refers to the <a href="/facts/Gaussian_hypergeometric_series/yTEC6NBJ">Gaussian hypergeometric series</a>. Generalized hypergeometric functions include the (Gaussian) <a href="/facts/Hypergeometric_function/yTEC6NBJ">hypergeometric function</a> and the <a href="/facts/Confluent_hypergeometric_function/D0FxgWUa">confluent hypergeometric function</a> as special cases, which in turn have many particular <a href="/facts/Special_functions/JETSeucA">special functions</a> as special cases, such as <a href="/facts/Elementary_functions/wVFyDwu8">elementary functions</a>, <a href="/facts/Bessel_function/hSyvFPqC">Bessel functions</a>, and the <a href="/facts/Orthogonal_polynomials/9cyRbDYU">classical orthogonal polynomials</a>.

Generalized hypergeometric function open-in-new

Generalized hypergeometric function