Abstract
A generalized binomial theorem is developed in terms of Bell polynomials and by applying this identity some sums involving inverse binomial coefficient are calculated. A technique is derived for calculating a class of hypergeometric transformation formulas and also some curious q series identities.
Highlights
Some of the most recent developments are on the use of different techniques for obtaining sums of hypergeometric series
We will use the theorems of this paper to prove some series identities related to the Hurwitz Zeta function and generalize a new theorem
By using the same techniques derived in this paper one can find various hypergeometric transformation formulas and their q-analog
Summary
Some of the most recent developments are on the use of different techniques for obtaining sums of hypergeometric series. Making use of certain special properties of Bell polynomials we can evaluate successive derivative of a given function. Differentiating (13) m times with respect to r and considering the case r = n, where r is a positive integer as well as using the definition from (15), we can derive dm drm
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