Generalization of a Quadratic Transformation Formula due to Gauss

Medhat A. Rakha

International Journal of Mathematics and Mathematical Sciences, 2012, vol. 2012, 1-16

Abstract:

The aim of this research paper is to obtain explicit expressions of ( 1 − ð ‘¥ ) 2 − 2 ð ‘Ž ð ¹ 1 [ ð ‘Ž , ð ‘ ; − 4 ð ‘¥ / ( 1 − ð ‘¥ ) 2 2 ð ‘ + ð ‘— ] for ð ‘— = 0 , ± 1 , ± 2 . For ð ‘— = 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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:789519

DOI: 10.1155/2012/789519

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