Generalization of a quadratic transformation formula due to gauss

Medhat A. Rakha

doi:10.1155/2012/789519

Generalization of a quadratic transformation formula due to gauss

Medhat A. Rakha^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The aim of this research paper is to obtain explicit expressions of (1-x) ^-2 a 2 F ₁ [ ^{a, b} _2b+f; - 4 x / (1 - x) ²] for j = 0, ± 1, ± 2. For j = 0, we have the well-known transformation formula due to Gauss. The results are derived with the help of generalized Watson's theorem. Some known results obtained earlier follow special cases of our main findings.

Original language	English
Article number	789519
Journal	International Journal of Mathematics and Mathematical Sciences
Volume	2012
DOIs	https://doi.org/10.1155/2012/789519
Publication status	Published - 2012

ASJC Scopus subject areas

Mathematics (miscellaneous)

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10.1155/2012/789519

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title = "Generalization of a quadratic transformation formula due to gauss",

abstract = "The aim of this research paper is to obtain explicit expressions of (1-x) -2 a 2 F 1 [ a, b 2b+f; - 4 x / (1 - x) 2] for j = 0, ± 1, ± 2. For j = 0, we have the well-known transformation formula due to Gauss. The results are derived with the help of generalized Watson's theorem. Some known results obtained earlier follow special cases of our main findings.",

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AB - The aim of this research paper is to obtain explicit expressions of (1-x) -2 a 2 F 1 [ a, b 2b+f; - 4 x / (1 - x) 2] for j = 0, ± 1, ± 2. For j = 0, we have the well-known transformation formula due to Gauss. The results are derived with the help of generalized Watson's theorem. Some known results obtained earlier follow special cases of our main findings.

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Generalization of a quadratic transformation formula due to gauss

Abstract

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