Some unified and generalized Kummer's first summation theorems with applications in Laplace transform technique (Q326938)
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scientific article; zbMATH DE number 6637981
| Language | Label | Description | Also known as |
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| English | Some unified and generalized Kummer's first summation theorems with applications in Laplace transform technique |
scientific article; zbMATH DE number 6637981 |
Statements
Some unified and generalized Kummer's first summation theorems with applications in Laplace transform technique (English)
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12 October 2016
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Summary: Some significant hypergeometric summation theorems with suitable convergence conditions are obtained in the present study, which are analogous to Kummer's summation theorem \({_2F_1(-1)}\) recorded by Prudnikov et al. and derived by Choi, Kim et al., Rakha-Rathie and Rathie-Kim. By means of these summation theorems we also find the Laplace transforms of Kummer's confluent hypergeometric function \(_1F_1\) in closed form.
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beta and gamma functions
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Gauss and Kummer hypergeometric functions
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Legendre duplication formula
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principle of analytic continuation
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Laplace transforms
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