Remarks on a summation formula for three-variables hypergeometric function X8 and certain hypergeometric transformations
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The first object of this note is to show that a summation formula due to Padmanabham for three-variables hypergeometric function X8 introduced by Exton can be proved in a different (from Padmanabham's and his observation) yet, in a sense, conventional method, which has been employed in obtaining a variety of identities associated with hypergeometric series. The second purpose is to point out that one of two seemingly new hypergeometric identities due to Exton was already recorded and the other one is easily derivable from the first one. A corrected and a little more compact form of a general transform involving hypergeometric functions due to Exton is also given.
Abstract
The first object of this note is to show that a summation formula due to Padmanabham for three-variables hypergeometric function X8 introduced by Exton can be proved in a different (from Padmanabham's and his observation) yet, in a sense, conventional method, which has been employed in obtaining a variety of identities associated with hypergeometric series. The second purpose is to point out that one of two seemingly new hypergeometric identities due to Exton was already recorded and the other one is easily derivable from the first one. A corrected and a little more compact form of a general transform involving hypergeometric functions due to Exton is also given.
참고문헌 (13)
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