Appell-type extension of the $_pR_q(\nu,\tau;z)$ function
DOI:
https://doi.org/10.5269/bspm.64070Resumen
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.
Referencias
1. Bailey W. N., Generalized hypergeometric series, second edition, Cambridge Mathematical Tract, No. 32, Cambridge University Press, Cambridge, (1964).
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).
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).
Descargas
Publicado
2025-09-17
Número
Sección
Research Articles
Licencia
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
Cómo citar
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
