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On an extension of a quadratic transformation formula due to Kummer

Medhat A. Rakha ; athematics Department, Faculty of Science, Suez Canal University, Ismailia 41 522, Egypt
Navratna Rathie ; Department of Mathematics, Rajasthan Technical University, Kota-324 010, Rajasthan,India
Purnima Chopra ; Department of Mathematics, Marudhar Engineering College Raisar, NH-11, Jaipur Road,Bikaner-334 001, Rajasthan, India


Puni tekst: engleski pdf 151 Kb

str. 207-209

preuzimanja: 844

citiraj


Sažetak

The aim of this research note is to prove the following new transformation formula
(1x)2a3F2[a,a+12,d+1;x2(1x)2c+32,d]=4F3[2a,c,2d+12A+12,2d12A+12;2x2c+2,2d+12A12,2d12A12]
valid for |x|<12 and if |x|=12,
then Re(c2a)>0, where A=16d216cd8d+1. For d=c+12,
we get quadratic transformations due to Kummer. The result is derived with the help of the
generalized Gauss's summation theorem available in the literature.

Ključne riječi

quadratic transformation formula; Kummer transformation; Gauss summation theorem

Hrčak ID:

43997

URI

https://hrcak.srce.hr/43997

Datum izdavanja:

9.12.2009.

Posjeta: 1.562 *

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