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Generalization of a Quadratic Transformation Formula due to Gauss

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  • Medhat A. Rakha

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.

Suggested Citation

  • Medhat A. Rakha, 2012. "Generalization of a Quadratic Transformation Formula due to Gauss," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-16, August.
    • Handle: RePEc:hin:jijmms:789519
    DOI: 10.1155/2012/789519
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