CERTAIN SUMMATION FORMULAS FOR HUMBERT’S DOUBLE HYPERGEOMETRIC SERIES Ψ2 AND Φ2
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The main objective of this paper is to establish certain explicit expressions for the Humbert functions $$ \Phi_2 (a,\,a+i\,;\,c\,;\,x,\,-x) \quad \text{and} \quad \Psi_2 (a\,;\, c,\,c+i\,;\,x,\,-x)$$ for $i=0,\, \pm 1,\, \pm 2,\, \ldots,\, \pm 5$. Several new and known summation formulas for $\Phi_2$ and $\Psi_2$ are considered as special cases of our main identities.
Abstract
The main objective of this paper is to establish certain explicit expressions for the Humbert functions $$ \Phi_2 (a,\,a+i\,;\,c\,;\,x,\,-x) \quad \text{and} \quad \Psi_2 (a\,;\, c,\,c+i\,;\,x,\,-x)$$ for $i=0,\, \pm 1,\, \pm 2,\, \ldots,\, \pm 5$. Several new and known summation formulas for $\Phi_2$ and $\Psi_2$ are considered as special cases of our main identities.
참고문헌 (10)
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