Abstract
The aim of this paper is to establish a general form of Kummer's second-type summation theory. By defining a new form for the divided of the Pochhammer symbol ((d + i)(n)/(d)(n)), we can develop a general form of Kummer's second-type summation theorem as e(2)(-(x/2))F(2)
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in the form of a sum of e(-(x/2)) F-1(1)
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for i, l = 0, 1, 2, ..., Then, some properties of the generalized Kummer's second-type summation theorem can yield a number of known and novel results.