GENERALIZATION OF A QUADRATIC TRANSFORMATION DUE TO EXTON

Yong Sup Kim, Gradimir V. Milovanović, Arjun K. Rathie, Richard B. Paris

DOI Number
https://doi.org/10.22190/FUMI210811085K
First page
927
Last page
938

Abstract


Exton [Ganita {\bf54} (2003), 13--15] obtained numerous new quadratic transformations involving hypergeometric functions of order two and of higher order by applying various known classical summation theorems to a general transformation formula based on the Bailey transformation. We obtain a generalization of one of the Exton quadratic transformations. The results are derived with the help of a generalization of Dixon's summation theorem for the series ${}_3F_2$ obtained earlier by Lavoie {\em et al.} Several interesting known as well as new special cases and limiting cases are also given.

Keywords

Quadratic transformation, hypergeometric function of order two, generalized classical Dixon's theorem

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References


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DOI: https://doi.org/10.22190/FUMI210811085K

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