Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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ON A NEW CLASS OF SERIES IDENTITIES

  • SHEKHAWAT, NIDHI (Research Scholar, Department of Mathematics & Statistics, Bansthali University) ;
  • CHOI, JUNESANG (Department of Mathematics, Dongguk University) ;
  • RATHIE, ARJUN K. (Department of Mathematics, School of Mathematical and Physical Sciences, Central University of Kerala) ;
  • PRAKASH, OM (Department of Mathematics, Indian Institute of Technology Patna)
  • Received : 2015.04.08
  • Accepted : 2015.07.24
  • Published : 2015.09.25
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Abstract

We aim at giving explicit expressions of $${\sum_{m,n=0}^{{\infty}}}{\frac{{\Delta}_{m+n}(-1)^nx^{m+n}}{({\rho})_m({\rho}+i)_nm!n!}$$, where i = 0, ${\pm}1$, ${\ldots}$, ${\pm}9$ and $\{{\Delta}_n\}$ is a bounded sequence of complex numbers. The main result is derived with the help of the generalized Kummer's summation theorem for the series $_2F_1$ obtained earlier by Choi. Further some special cases of the main result considered here are shown to include the results obtained earlier by Kim and Rathie and the identity due to Bailey.

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References

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