Appell-Type Extension of The $_pR_q(\nu,\tau;z)$ Function
ATE pRq F
Abstract
In this paper, we define two variables Appell-type extension of the $_pR_q(\nu,\tau;z)$ function. Also, we obtain confluence formulas, double integral representations and differentiation formulas for the Appell-type extension of the $_pR_q(\nu,\tau;z)$ function.Downloads
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References
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\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{e2} A. Erd\'{e}lyi, H. Bateman, Higher transcendental functions. Vol. I, McGraw-Hill, New York, (1953).
\bibitem{m1} G. M. Mittag-Leffler, Sur la nouvelle fonction $ E_{\alpha } \left( x \right) $, C. R. Acad. Sci. Paris, 137 (1903), 554-558.
\bibitem{p2} T. R. Prabhakar, A singular integral equation with a generalized Mittag-Leffler function in the Kernel, Yokohama Math. J., 19(1971), 7-15.
\bibitem{r1} E. D. Rainville, Special Functions, Mcmillan, New York, (1960).
\bibitem{s1} R. K. Saxena, S. L. Kalla, R. Saxena, On a multivariate analogue of generalized Mittag-Leffler function, Integral Transforms Spec Funct., 22(7) (2011), 533-548.
\bibitem{s2} K. Sharma, Application of fractional calculus operators to related areas, Gen 7(1) (2011), 33–40.
\bibitem{s3} M. Sharma, R. Jain, A note on a generalized M-series as a special function of fractional calculus, Fract. Calc. Appl. Anal., 12(4) (2009), 449–452.
\bibitem{w1} A. Wiman, Über den fundamental Satz in der Theorie der Funktionen $ E_{\alpha } \left( x \right) $, Acta Math., 29 (1905), 191-201.
\bibitem{w2} E. M. Wright, The generalized bessel function of order greater than one, Quarterly Journal of Mathematics, 11(1) (1940), 36-48.
Published
2025-09-17
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