Eulerian integral formulas and associated fractional integration (Q2724876)
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scientific article; zbMATH DE number 1618336
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Eulerian integral formulas and associated fractional integration |
scientific article; zbMATH DE number 1618336 |
Statements
7 November 2002
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Eulerian integral
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multivariable polynomials
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multivariable \(H\)-function
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fractional integration
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Eulerian integral formulas and associated fractional integration (English)
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The paper under review evaluates certain Eulerian type integrals which makes use of the familiar formula NEWLINE\[NEWLINE\int(x-a)^{\rho-1}(b-x)^{\sigma-1}dx= {\Gamma(\rho) \Gamma(\sigma) \over\Gamma (\rho+ \sigma)}(b-a)^{\rho +\sigma-1}, NEWLINE\]NEWLINE NEWLINE\[NEWLINE\bigl(\text{Re} (\rho)>0;\;\text{Re}(sigma) >0;\;a\neq b\bigr).NEWLINE\]NEWLINE Several product combinations are involved in the integrand which include multivariable polynomial system [\textit{H. M. Srivastava}, Pac. J. Math. 117, 183-191 (1985; Zbl 0533.33003)] and the well known \(H\)-function of several variables. The results are quite involved and loaded with parameters, and therefore are not cited here.
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