Paper Title:

Two Further Methods for Deriving Four Results Contiguous to Kummer's Second Theorem

Author(s):

I. Kim and J. Kim

Department of Mathematics Education,
Wonkwang University,
Iksan, 570-749,
Korea.
E-mail: iki@wku.ac.kr  

Department of Mathematics Education,
Wonkwang University,
Iksan, 570-749,
Korea.
E-mail: joohyung@wku.ac.kr
 

Abstract:

In the theory of generalized hypergeometric function, transformation and summation formulas play a key role. In particular, in one of the Kummer's transformation formulas, Kim, et al. in 2012, have obtained ten contiguous results in the form of a single result with the help of generalization of Gauss's second summation theorem obtained earlier by Lavoie, et al.. In this paper, we aim at presenting four of such results by the technique of contiguous function relations and integral method developed by MacRobert.

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