Functional relations involving Saran's hypergeometric functions \(F_E\) and \(F^{(3)}\) (Q2917725)
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scientific article; zbMATH DE number 6088973
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Functional relations involving Saran's hypergeometric functions \(F_E\) and \(F^{(3)}\) |
scientific article; zbMATH DE number 6088973 |
Statements
1 October 2012
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generalized hypergeometric series
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Saran's hypergeometric functions
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Bessel's functions
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Kelvin's functions
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Srivastava's hypergeometric functions
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Functional relations involving Saran's hypergeometric functions \(F_E\) and \(F^{(3)}\) (English)
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The authors consider the generalized Appell's function \(F_{E}(a;b_{1},b_{2};c_{1},c_{2}, c_{3};x,y,z)\). This is known as Saran's hypergeometric function and it is a function of hypergeometric type of three variables, \(x,y,z\). The authors split the function \(F_{E}\) into eight parts and show some relations between this function and Srivastava's hypergeometric function \(F^{(3)}\). Some particular cases are also presented. The authors obtain as special cases of their formulas several relations between the familiar hypergeometric functions \(\Psi_{2}\), \(_{0}F_{1},\;_{1}F_{1}, \;_{0}F_{3}\).
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