Fourier transform representation of the generalized hypergeometric functions with applications to the confluent and Gauss hypergeometric functions
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摘要
We present a Fourier transform representation of the generalized hypergeometric functions. We then use this representation to evaluate integrals of products of two generalized hypergeometric functions. A number of integral identities for confluent and Gauss hypergeometric functions are presented. The results for Euler’s gamma function are deduced as special cases.
论文关键词：Hypergeometric and confluent hypergeometric functions,Generalized hypergeometric function,Kampé de Fériet function,Fourier transform,Parseval’s identity,Distributional representation
论文评审过程：Received 10 February 2015, Revised 12 April 2015, Accepted 23 April 2015, Available online 21 May 2015, Version of Record 21 May 2015.
论文官网地址：https://doi.org/10.1016/j.amc.2015.04.083
