ScholarLens Back to search
2009•Unpublished venueRequires access

REMARKS ON A SUMMATION FORMULA FOR THREE-VARIABLES HYPERGEOMETRIC FUNCTION $X_8$ AND CERTAIN HYPERGEOMETRIC TRANSFORMATIONS

Junesang Choi, Arjun K. Rathie, H. Harsh

Open publisher page 3 citations

Abstract

Abstract. The first object of this note is to show that a summation for-mula due to Padmanabham for three-variables hypergeometric function X8 introduced by Exton can be proved in a different (from Padmanab-ham’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 cor-rected and a little more compact form of a general transform involving hypergeometric functions due to Exton is also given. 1. Introduction and

About this research paper

What this paper is about

Abstract. The first object of this note is to show that a summation for-mula due to Padmanabham for three-variables hypergeometric function X8 introduced by Exton can be proved in a different (from Padmanab-ham’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 cor-rected and a little more compact form of a general transform involving hypergeometric functions due to Exton is also given. 1. Introduction and

Why it matters

OpenAlex reports 3 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Abstract. The first object of this note is to show that a summation for-mula due to Padmanabham for three-variables hypergeometric function X8 introduced by Exton can be proved in a different (from Padmanab-ham’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 cor-rected and a little more compact form of a general transform involving hypergeometric functions due to Exton is also given. 1. Introduction and

Key concepts: Basic hypergeometric series, Generalized hypergeometric function, Hypergeometric function of a matrix argument, Hypergeometric identity, Bilateral hypergeometric series, Confluent hypergeometric function, Mathematics, Lauricella hypergeometric series

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
REMARKS ON A SUMMATION FORMULA FOR THREE-VARIABLES HYPERGEOMETRIC FUNCTION $X_8$ AND CERTAIN HYPERGEOMETRIC TRANSFORMATIONS — Research Paper | ScholarLens