Certain transformations and summations for generalized hypergeometric series with integral parameter differences

DOI10.1080/10652469.2010.498001zbMath1217.33013OpenAlexW2019999788MaRDI QIDQ3074594

Allen R. Miller, Richard B. Paris

Publication date: 9 February 2011

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://rke.abertay.ac.uk/en/publications/675d62d9-c63a-4233-9b99-4a39df534984

zbMATH Keywords

generalized hypergeometric seriesquadratic transformationsummation theorems

Mathematics Subject Classification ID

Generalized hypergeometric series, ({}_pF_q) (33C20) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15)

Related Items (12)

The Clausenian hypergeometric function \({}_3 F_2\) with unit argument and negative integral parameter differences ⋮ Fractional integral operators characterized by some new hypergeometric summation formulas ⋮ New properties of a certain method of summation of generalized hypergeometric series ⋮ Generalization of a summation formula due to fox ⋮ A contiguous extension of Dixon’s theorem for a terminating 4F3(1) series with applications ⋮ Unnamed Item ⋮ Transformation formulas for the generalized hypergeometric function with integral parameter differences ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Extensions of the classical theorems for very well-poised hypergeometric functions ⋮ Extension of some classical summation theorems for the generalized hypergeometric series with integral parameter differences ⋮ Some summation theorems for Clausen's hypergeometric functions with unit argument

Cites Work

• On the zeros of some generalized hypergeometric functions
• Certain summation and transformation formulas for generalized hypergeometric series
• Karlsson–Minton summation theorems for the generalized hypergeometric series of unit argument

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