Summation formulas for the function ${R_1}\left[ {\mu,\delta,\delta';\gamma;\nu ,\tau ,{z_1},{z_2}} \right]$
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In this paper, we obtain finite and infinite summation formulas for Appell-type extension of $_pR_q(\nu,\tau;z)$ function, denoted as ${R_1}\left[ {\mu,\delta,\delta';\gamma;\nu ,\tau ,{z_1},{z_2}} \right]$ and confluent functions $R{\Phi _1}\left[ {\mu,\delta;\gamma;\nu ,\tau ,{z_1},{z_2}} \right], R{\Phi _2}\left[ {\delta,\delta';\gamma;\nu ,\tau ,{z_1},{z_2}} \right]$ and $R{\Phi _3}\left[ {\delta;\gamma;\nu ,\tau ,{z_1},{z_2}} \right].$Downloads
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Referências
\bibitem{y1} Yu. A. Brychkov, N. Saad, Some formulas for the Appell function $F_1(a; b; b'; c;w; z)$, Integral Transform Spec Funct., 23(11)(2012), 793-802.
\bibitem{d1} R. Desai, A. K. Shukla, Some results on function ${}_p{R_q}(\alpha ,\beta ;z)$, J. Math. Anal. Appl., 448(1)(2017), 187-197.
\bibitem{d2} R. Desai, A. K. Shukla, Note on the ${}_pR_q(\alpha,\beta; z)$ function, J. Indian Math. Soc., 88(3-4) (2021), 288-297.
\bibitem{r1} E. D. Rainville, Special Functions, Mcmillan, New York, (1960).
\bibitem{t1} Y. M. Thakkar, A. K. Shukla, Some results involving the $_pR_q(\alpha,\beta;z)$ Function, J. Indian Math. Soc., Accepted for publication.
\bibitem{t2} Y. M. Thakkar, A. K. Shukla, Appell-Type Extension of The $_pR_q(\alpha,\beta;z)$ Function, Communicated for publication.
\bibitem{t3} Y. M. Thakkar, A. K. Shukla, Some Formulas For The Function ${R_1}\left[ {\mu,\delta,\delta';\gamma;\nu ,\tau ,{z_1},{z_2}} \right]$, Communicated for publication.
\bibitem{w1} X. Wang, Infinite summatition formulas of double hypergeometric functions, Integral Transform Spec Funct., 27(5)(2015), 347-364.
\bibitem{d1} R. Desai, A. K. Shukla, Some results on function ${}_p{R_q}(\alpha ,\beta ;z)$, J. Math. Anal. Appl., 448(1)(2017), 187-197.
\bibitem{d2} R. Desai, A. K. Shukla, Note on the ${}_pR_q(\alpha,\beta; z)$ function, J. Indian Math. Soc., 88(3-4) (2021), 288-297.
\bibitem{r1} E. D. Rainville, Special Functions, Mcmillan, New York, (1960).
\bibitem{t1} Y. M. Thakkar, A. K. Shukla, Some results involving the $_pR_q(\alpha,\beta;z)$ Function, J. Indian Math. Soc., Accepted for publication.
\bibitem{t2} Y. M. Thakkar, A. K. Shukla, Appell-Type Extension of The $_pR_q(\alpha,\beta;z)$ Function, Communicated for publication.
\bibitem{t3} Y. M. Thakkar, A. K. Shukla, Some Formulas For The Function ${R_1}\left[ {\mu,\delta,\delta';\gamma;\nu ,\tau ,{z_1},{z_2}} \right]$, Communicated for publication.
\bibitem{w1} X. Wang, Infinite summatition formulas of double hypergeometric functions, Integral Transform Spec Funct., 27(5)(2015), 347-364.
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2025-09-01
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