On an extension of Kummer's second theorem

Medhat A. Rakha, Mohamed M. Awad, Arjun K. Rathie

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Abstract

The aim of this paper is to establish an extension of Kummer's second theorem in the form e - x / 2 F 2 2 [ a, 2 + d; x 2 a + 2, d; ] = F 1 0 [ -; x 2 / 16 a + 3 / 2; ] + ((a / d - 1 / 2) / (a + 1)) x F 1 0 [ -; x 2 / 16 a + 3 / 2; ] + (c x 2 / 2 (2 a + 3)) F 1 0 [ -; x 2 / 16 a + 5 / 2; ], where c = 1 / a + 1 1 / 2 - a / d + a / d (d + 1), d ≠ 0, - 1, - 2,. For d = 2 a, we recover Kummer's second theorem. The result is derived with the help of Kummer's second theorem and its contiguous results available in the literature. As an application, we obtain two general results for the terminating F 2 3 (2) series. The results derived in this paper are simple, interesting, and easily established and may be useful in physics, engineering, and applied mathematics.

Original languageEnglish
Article number128458
JournalAbstract and Applied Analysis
Volume2013
DOIs
Publication statusPublished - 2013

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ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

On an extension of Kummer's second theorem. / Rakha, Medhat A.; Awad, Mohamed M.; Rathie, Arjun K.

In: Abstract and Applied Analysis, Vol. 2013, 128458, 2013.

Research output: Contribution to journalArticle

Rakha, Medhat A. ; Awad, Mohamed M. ; Rathie, Arjun K. / On an extension of Kummer's second theorem. In: Abstract and Applied Analysis. 2013 ; Vol. 2013.
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