### 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 language | English |
---|---|

Article number | 128458 |

Journal | Abstract and Applied Analysis |

Volume | 2013 |

DOIs | |

Publication status | Published - 2013 |

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### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Abstract and Applied Analysis*,

*2013*, [128458]. https://doi.org/10.1155/2013/128458

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

Research output: Contribution to journal › Article

*Abstract and Applied Analysis*, vol. 2013, 128458. https://doi.org/10.1155/2013/128458

}

TY - JOUR

T1 - On an extension of Kummer's second theorem

AU - Rakha, Medhat A.

AU - Awad, Mohamed M.

AU - Rathie, Arjun K.

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84877291371&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84877291371&partnerID=8YFLogxK

U2 - 10.1155/2013/128458

DO - 10.1155/2013/128458

M3 - Article

VL - 2013

JO - Abstract and Applied Analysis

JF - Abstract and Applied Analysis

SN - 1085-3375

M1 - 128458

ER -