On Hypergeometric Functions and Generalizations of Legendre's Relation |
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| Authors: | EA Karatsuba M Vuorinen |
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| Institution: | a Computer Centre of RAS, ul. Vavilova 40, Moscow, 117967, Russiaf1;b Department of Mathematics, University of Helsinki, Yliopistonkatu 5, 00014, Helsinki, Finlandf2 |
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| Abstract: | We prove some convexity properties for a sum of hypergeometric functions and obtain a generalization of Legendre's relation for complete elliptic integrals. We apply these results to prove some inequalities for hypergeometric functions, incomplete beta-functions, and Legendre functions. |
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| Keywords: | Gaussian hypergeometric functions |
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