Some reduction and transformation formulas for the Appell hypergeometric function \(F_{2}\) (Q1763410)
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scientific article; zbMATH DE number 2136278
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some reduction and transformation formulas for the Appell hypergeometric function \(F_{2}\) |
scientific article; zbMATH DE number 2136278 |
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Some reduction and transformation formulas for the Appell hypergeometric function \(F_{2}\) (English)
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22 February 2005
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In the present paper the authors obtain several finite algebraic sum representations of the Appell's second series \(F_2(s,a_1,a_2;b_1,b_2;x,y)\) in the case when \(s,a_1,a_2,b_1\) and \(b_2\) are positive integers. These finite-sum expansions are given in terms of the hypergeometric functions \(_2F_1\) and \(_3F_2\). They also include a list of some useful reduction (and transformation) formulas. Finally, some potential applications are discussed.
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multiple hypergeometric functions
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Appell series, hypergeometric series
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