Certain new summation formulas for the series \(_4F_3 (1)\) with applications
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Authors
Junesang Choi
- Department of Mathematics, Dongguk University, Gyeongju 38066, Republic of Korea.
Arjun K. Rathie
- Department of Mathematics, School of Mathematical and Physical Sciences, Central University of Kerala, Riverside Transit Campus, Padennakkad P. O. Nileshwar, Kasaragod 671 328, Kerala, India.
Abstract
The main objective of this paper is to provide thirteen (presumably) new summation formulas for
the series \(_4F_3\) of unit argument expressed in terms of Gamma functions. As special cases of our main
results, we also present twenty four summation formulas for the terminating \(_4F_3 (1)\), whose further special
cases are derived to give thirty two known summation formulas for the terminating \(_4F_3 (1)\). The results
presented here are established with the help of a general result recorded in the book of Prudnikov et al.
and the generalization of Watson's summation theorem obtained earlier by Lavoie et al.
Share and Cite
ISRP Style
Junesang Choi, Arjun K. Rathie, Certain new summation formulas for the series \(_4F_3 (1)\) with applications, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 4722--4736
AMA Style
Choi Junesang, Rathie Arjun K., Certain new summation formulas for the series \(_4F_3 (1)\) with applications. J. Nonlinear Sci. Appl. (2016); 9(6):4722--4736
Chicago/Turabian Style
Choi, Junesang, Rathie, Arjun K.. "Certain new summation formulas for the series \(_4F_3 (1)\) with applications." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 4722--4736
Keywords
- Gamma function
- Pochhammer symbol
- generalized hypergeometric function
- Watson's summation theorem
- generalized Watson's summation theorem.
MSC
References
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