Summation formulas for the function R1 [µ, δ, δ′; γ; ν, Ï„, z1, z2]
DOI:
https://doi.org/10.5269/bspm.64982Abstract
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 $R{\Phi _3}\left[ {\delta;\gamma;\nu ,\tau ,{z_1},{z_2}} \right].$
References
1. Brychkov Yu A. and Saad N., Some formulas for the Appell function F1(a; b; b′; c; w; z), Integral Transform Spec Funct. 23(11), 793-802, (2012).
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. Rainville E. D., Special Functions, The Macmillan Company, New York, (1960).
6. 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.
7. Thakkar Y. M. and Shukla A. K., Appell-Type Extension of The pRq(α, β; z) Function, Communicated for publication.
8. Thakkar Y. M. and Shukla A. K., Some Formulas For The Function R1 [µ, δ, δ′; γ; ν, Ï„, z1, z2], Communicated for publication.
9. Thakkar Y. M. and Shukla A. K., Some Formulas For The Function R3[µ, µâ€²Î´, δ′; γ; ν, Ï„, z1, z2], Advanced Studies: Euro-Tbilisi Mathematical Journal 16(3), 53–66, (2023).
10. Wang X., Infinite summatition formulas of double hypergeometric functions, Integral Transform Spec Funct., 27(5), 347-364 (2015).
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. Rainville E. D., Special Functions, The Macmillan Company, New York, (1960).
6. 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.
7. Thakkar Y. M. and Shukla A. K., Appell-Type Extension of The pRq(α, β; z) Function, Communicated for publication.
8. Thakkar Y. M. and Shukla A. K., Some Formulas For The Function R1 [µ, δ, δ′; γ; ν, Ï„, z1, z2], Communicated for publication.
9. Thakkar Y. M. and Shukla A. K., Some Formulas For The Function R3[µ, µâ€²Î´, δ′; γ; ν, Ï„, z1, z2], Advanced Studies: Euro-Tbilisi Mathematical Journal 16(3), 53–66, (2023).
10. Wang X., Infinite summatition formulas of double hypergeometric functions, Integral Transform Spec Funct., 27(5), 347-364 (2015).
Downloads
Published
2025-09-01
Issue
Section
Research Articles
License
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).
