On a representation of Humbert's double hypergeometric series $\Phi_3$ in a series of Gauss's $_2F_1$ function

Arjun K. Rathie; Harsh Vardhan Harsh; Victor V. Manako

arxiv: 1605.01820 · v1 · pith:WGUNL2WMnew · submitted 2016-05-06 · 🧮 math.CV

On a representation of Humbert's double hypergeometric series Φ₃ in a series of Gauss's ₂F₁ function

Arjun K. Rathie , Victor V. Manako , Harsh Vardhan Harsh This is my paper

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keywords seriesdoublefunctiongaussgivenhumberthypergeometricrepresentation

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Very recently a new series representation of Humbert's double hypergeometric series $\Phi_3$ in series of Gauss's $_2F_1$ function was given by one of us. The aim of this short research note is to provide an alternative proof of the result. A few interesting special cases are also given.

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On a representation of Humbert's double hypergeometric series Φ₃ in a series of Gauss's ₂F₁ function

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