TY - JOUR
T1 - On certain hypergeometric identities deducible by using the beta integral method
AU - Ibrahim, Adel K.
AU - Rakha, Medhat A.
AU - Rathie, Arjun K.
N1 - Funding Information:
The authors are thankful to the referee for making certain very useful suggestions. The work of this research paper was supported by the research grant (05/4/33) funded by Jazan University - Jazan, Saudi Arabia.
PY - 2013/11
Y1 - 2013/11
N2 - The aim of this research paper is to demonstrate how one can obtain eleven new and interesting hypergeometric identities (in the form of a single result) from the old ones by mainly applying the well-known beta integral method which was used successfully and systematically by Krattenthaler and Rao in their well known, very interesting research papers. The results are derived with the help of generalization of a quadratic transformation formula due to Kummer very recently obtained by Kim et al. Several identities, including one obtained earlier by Krattenthaler and Rao, follow special cases of our main findings. The results established in this paper are simple, interesting, easily established and may be potentially useful.
AB - The aim of this research paper is to demonstrate how one can obtain eleven new and interesting hypergeometric identities (in the form of a single result) from the old ones by mainly applying the well-known beta integral method which was used successfully and systematically by Krattenthaler and Rao in their well known, very interesting research papers. The results are derived with the help of generalization of a quadratic transformation formula due to Kummer very recently obtained by Kim et al. Several identities, including one obtained earlier by Krattenthaler and Rao, follow special cases of our main findings. The results established in this paper are simple, interesting, easily established and may be potentially useful.
KW - Beta integral
KW - Hypergeometric series
KW - Kummer summation theorem
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U2 - 10.1186/1687-1847-2013-341
DO - 10.1186/1687-1847-2013-341
M3 - Article
AN - SCOPUS:84897830108
SN - 1687-1839
VL - 2013
JO - Advances in Difference Equations
JF - Advances in Difference Equations
M1 - 341
ER -