Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2023; 38(3): 807-819

Online first article April 24, 2023      Printed July 31, 2023

https://doi.org/10.4134/CKMS.c220217

Copyright © The Korean Mathematical Society.

A note on certain transformation formulas related to Appell, Horn and Kamp\'{e} de F\'{e}riet functions

Asmaa Orabi Mohammed, Medhat Ahmed Rakha, Arjun K. Rathie

Suez Canal University; Suez Canal University; Village: Tulsi, Post: Jakhmund, District: BUNDI-323021

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In 2019, Mathur and Solanki \cite{7,8} obtained a few transformation formulas for Appell, Horn and the Kamp\'{e} de F\'{e}riet functions. Unfortunately, some of the results are well-known and very old results in literature while others are erroneous. Thus the aim of this note is to provide the results in corrected forms and some of the results have been written in more compact form.

Keywords: Hypergeometric function, Kummer's second theorem, contiguous results, Appell's series, Horn's function, Kamp\'{e} de F\'{e}riet function

MSC numbers: Primary 33B15, 33C05, 33C15; Secondary 33C65, 33C20

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