Regularized Hypergeometric Function

Given a hypergeometric or generalized hypergeometric function _pF_q(a_1,...,a_p;b_1,...,b_q;z), the corresponding regularized hypergeometric function is defined by

where Gamma(z) is a gamma function. Regularized hypergeometric functions are implemented in the Wolfram Language as the functions Hypergeometric0F1Regularized [b, z], Hypergeometric1F1Regularized [a, b, z], Hypergeometric2F1Regularized [a, b, c, z], and in general, HypergeometricPFQRegularized [{a1, ...ap}, {b1, ..., bq}, z].

See also

Confluent Hypergeometric Function of the First Kind, Confluent Hypergeometric Function of the Second Kind, Confluent Hypergeometric Limit Function, Generalized Hypergeometric Function, Hypergeometric Function

Related Wolfram sites

http://functions.wolfram.com/HypergeometricFunctions/Hypergeometric0F1Regularized/, http://functions.wolfram.com/HypergeometricFunctions/Hypergeometric1F1Regularized/, http://functions.wolfram.com/HypergeometricFunctions/Hypergeometric2F1Regularized/, http://functions.wolfram.com/HypergeometricFunctions/HypergeometricPFQRegularized/

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Cite this as:

Weisstein, Eric W. "Regularized Hypergeometric Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RegularizedHypergeometricFunction.html

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