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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.
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참고문헌 (10)
참고문헌 신청
A. K. Rathie / 2013 / On representation of Humbert’s double hypergeometric series in a series of Gauss’s 2F1 function / arXiv: 1312.0064v1
A. P. Prudnikov / 1990 / Integrals and Series. Vol. 3 / Gordon and Breach Science Publishers
E. D. Rainville / 1971 / Special Functions / Macmillan Company
H. M. Srivastava / 1984 / A Treatise on Generating Functions / Halsted Press
H. M. Srivastava / 2012 / Zeta and q-Zeta Functions and Associated Series and Integrals / Elsevier Science Publishers
A. P. Prudnikov / 1990 / Integrals and Series. Vol. 3 / Gordon and Breach Science Publishers
E. D. Rainville / 1971 / Special Functions / Macmillan Company
H. M. Srivastava / 1984 / A Treatise on Generating Functions / Halsted Press
H. M. Srivastava / 2012 / Zeta and q-Zeta Functions and Associated Series and Integrals / Elsevier Science Publishers
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