Appell-type extension of the $_pR_q(\nu,\tau;z)$ function
DOI:
https://doi.org/10.5269/bspm.64070Abstract
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.
References
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2. Desai R. and Shukla A. K., Some results on function pRq(α, β; z), J. Math. Anal. Appl. 448, 187-197, (2017).
3. Desai R. and Shukla A. K., Note on the pRq(α, β; z) function, J. Indian Math. Soc. 88(3-4), 288-297, (2021).
4. Erdelyi A. and Bateman H., Higher Transcendental Functions vol. I, McGraw-Hill, New York, (1953).
5. Mittag-Leffler G. M., Sur la nouvelle fonction Eα (x), C. R. Acad. Sci. Paris, 137, 554-558, (1903).
6. Prabhakar T. R., A singular integral equation with a generalized Mittag-Leffler function in the Kernel, Yokohama Math. J., 19, 7-15, (1971).
7. Rainville E. D., Special Functions, The Macmillan Company, New York, (1960).
8. Saxena R. K., Kalla S. L. and Saxena R., On a multivariate analogue of generalized Mittag-Leffler function, Integral Transforms Spec Funct., 22(7), 533-548, (2011).
9. Sharma K., Application of fractional calculus operators to related areas, Gen 7(1), 33–40, (2011).
10. Sharma M. and Jain R., A note on a generalized M-series as a special function of fractional calculus, Fract. Calc. Appl. Anal., 12(4), 449–452, (2009).
11. Thakkar Y. M. and Shukla A. K., Some results involving the pRq(α, β; z) Function, J. Indian Math. Soc. 90(3-4), 329-342, (2023).
12. Wiman A., Uber den fundamental Satz in der Theorie der Funktionen ¨ Eα (x), Acta Math., 29, 191-201, (1905).
13. Wright E. M., The generalized bessel function of order greater than one, Quarterly Journal of Mathematics, 11(1), 36-48, (1940).
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Published
2025-09-17
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How to Cite
Thakkar, Y. M., & Shukla, A. K. (2025). Appell-type extension of the $_pR_q(\nu,\tau;z)$ function. Boletim Da Sociedade Paranaense De Matemática, 43, 1-13. https://doi.org/10.5269/bspm.64070
