Euler-type transformations for the generalized hypergeometric function \(_{r+2} F _{r+1}(x)\) (Q638652)
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scientific article; zbMATH DE number 5947336
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Euler-type transformations for the generalized hypergeometric function \(_{r+2} F _{r+1}(x)\) |
scientific article; zbMATH DE number 5947336 |
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Euler-type transformations for the generalized hypergeometric function \(_{r+2} F _{r+1}(x)\) (English)
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13 September 2011
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The authors provide generalizations of two of Euler's classical transformation formulas for the Gauss hypergeometric function extended to the case of the generalized hypergeometric function \(_{r+2}F_{r+1}(x)\) when there are additional numerator and denominator parameters differing by unity. The method employed to deduce the latter is also implemented to obtain a Kummer-type transformation formula for \(_{r+1}F_{r+1}(x)\).
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generalized hypergeometric function
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Euler transformation
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Kummer transformation
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