H_A^(τ_1,τ_2,τ_3 ) A Srivastava Hypergeometric Function

Recep Şahin; Oğuz Yağcı

EN

H_A^(τ_1,τ_2,τ_3 ) A Srivastava Hypergeometric Function

Abstract

Formulas and identities involving many well known special functions (such as the Gamma and Beta functions, Gauss hypergeometric function, and so on) play important roles in themselves and their diverse applications. In this paper, we will add τ1, τ2, τ3 parameters to the HA Srivastava hypergeometric function and we introduce new H τ1,τ2,τ3 A Srivastava’s triple τ -hypergeometric function. Then, we present some properties of the H τ1,τ2,τ3 A Srivastava’s triple τ -hypergeometric function In this paper, N, Z −, and C denote the sets of positive integers, negative integers, complex numbers, respectively. Also, N0 and Z represent the sets of positive integers and complex numbers by excluding origin, respectively. N0 := N ∪ {0} and Z − 0:= Z − ∪ {0} . The classical Gamma function Γ(x) is defined by [13, 16, 17, 19, 20

Keywords

Srivastava hypergeometric funtion, integral representation, derivative formula

References

[1] Agarwal, P., Certain properties of the generalized Gauss hypergeometric functions, Applied Mathematics & Information Sciences, 8(2014), no:5, 2315.
[2] Appell Kampé de Fériet, P.J., Fonctions Hypergéométriques et Hypersphériques, Gauthier-Villars, Paris, 1926.
[3] Al-Shammery, A.H. and Kalla, S.L., An extension of some hypergeometric functions of two variables, Rev. Acad. Canaria Cienc., 12 (2000), no. 1-2, 189-196.
[4] Choi, J. and Agarwal, P., Certain generating functions involving Appell series, Far East Journal of Mathematical Sciences, 84 (2014), no:1, 25-32.
[5] Choi, J., Parmar, R.K. and Chopra, P., The incomplete generalized 􀀀hypergeometric and second 􀀀Appell functions, Honam Math. J. 36 (2014), no. 3, 531-542.
[6] Çetinkaya, A., Ya˘gbasan, M.B. and Kıymaz, ˙I.O., The extended Srivastava’s hypergeometric function and their integral representation, J. Nonlinear sci. Appl., 9 (2016), no:6, 4860-4866.
[7] Exton, H., On Srivastava’s symmetrical triple hypergeometric function HB, J. Indian Acad. Math., 25 (2003), 17-22.
[8] Goswami, A., Jain, S., Agarwal, P. and Araci, S., A Note on the New Extended Beta and Gauss Hypergeometric Functions, Appl. Math, 12 (2018), no:1, 139-144.
[9] Hasanov, A., Srivastava H. M. and Turaev, M., Integral representation of Srivastava’s triple hypergeometric function, Taiwanese Journal of Mathematics, 15(2011), no. 6 , 2751-2762.
[10] Luo, M. J., Milovanovic, G. V. and Agarwal, P., Some results on the extended beta and extended hypergeometric functions. Applied Mathematics and Computation, 248 (2014), 631-651.

[11] Opps, S.B., Saad, N. and Srivastava, H.M., Some reduction and transformation formulas for the Appell hypergeometric function F2, J. Math. Anal. Appl., 302 (2005), no:1, 180-195.
[12] Opps, S.B., Saad, N. and Srivastava, H.M., Recursion formulas for Appell’s hypergeometric function F2 with some applications to radiation field problem, Appl. Math. Comput., 207 (2009), no:2, 545-558.
[13] Ruzhansky, M., Cho, Y. J.,Agarwal, P. and Area, I., Advances in Real and Complex Analysis with Applications, Springer Singapore, 2017.
[14] Parmar, R. K., Extended hypergeometric functions and associated properties, C. R. Math. Acad. Sci. Paris, 353 (2015), no:5, 421-426.
[15] Parmar, R. K. and Saxena, R. K., The incomplete generalized 􀀀-hypergeometric and second 􀀀-Appell functions, J. Korean Math. Soc. 53 (2016), no. 2, 363-379.
[16] Rainville, E.D., Special functions, Macmillan Company, New York, 1960; Reprinted by Chelsea Publishing Company, Bronx, New York, 1971.
[17] Slater, L.J. Generalized Hypergeometric Functions, Cambridge University Press, Cambridge, 1966.
[18] Srivastava, H.M., Hypergeometric functions of three variables, Ganita 15 (1964), no:2, 97-108.
[19] Srivastava, H.M. and Karlsson, P.W., Multiple Gaussian Hpergeometric Series, Halsted Press (John Wiley and Sons), New York, 1985.
[20] Srivastava, H.M. and Monacha, H.L., A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limited, Chichester),Wiley, New York, Chichester, Brisbane and Toronto, 1984.
[21] Srivastava, H.M., Some integrals representing triple hypergeometric functions , Rend. Circ. Mat. Palermo, 16 (1967), no:2, 99-115.
[22] Srivastava, H.M., Relations between functions contiguous to certain hypergeometric functions of three variables, Proc. Nat. Acad. Sci. India Sect. A, 36 (1966), 377-385.
[23] Şahin, R., Recursion Formulas for Srivastava Hypergeometric Functions. Mathematica Slovaca, 65 (2015), no:6, 1345-1360.
[24] Virchenko, N., Kalla, S. L. and Al-Zamel, A., Some results on a generalized hypergeometric function, Integral Transforms and Special Functions 12 (2001), no:1, 89-100.
[25] Virchenko, N., On some generalizations of the functions of hypergeometric type, Fract. Calc. Appl. Anal., 2 (1999), no. 3, 233-244.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Recep Şahin
0000-0001-5713-3830

Oğuz Yağcı
0000-0001-9902-8094

Publication Date

October 31, 2018

Submission Date

December 8, 2017

Acceptance Date

May 14, 2018

Published in Issue

Year 2018 Volume: 6 Number: 2

IZ

https://izlik.org/JA33NY27LC

APA

Şahin, R., & Yağcı, O. (2018). H_A^(τ_1,τ_2,τ_3 ) A Srivastava Hypergeometric Function. Mathematical Sciences and Applications E-Notes, 6(2), 1-9. https://izlik.org/JA33NY27LC

AMA

1.Şahin R, Yağcı O. H_A^(τ_1,τ_2,τ_3 ) A Srivastava Hypergeometric Function. Math. Sci. Appl. E-Notes. 2018;6(2):1-9. https://izlik.org/JA33NY27LC

Chicago

Şahin, Recep, and Oğuz Yağcı. 2018. “H_A^(τ_1,τ_2,τ_3 ) A Srivastava Hypergeometric Function”. Mathematical Sciences and Applications E-Notes 6 (2): 1-9. https://izlik.org/JA33NY27LC.

EndNote

Şahin R, Yağcı O (October 1, 2018) H_A^(τ_1,τ_2,τ_3 ) A Srivastava Hypergeometric Function. Mathematical Sciences and Applications E-Notes 6 2 1–9.

IEEE

[1]R. Şahin and O. Yağcı, “H_A^(τ_1,τ_2,τ_3 ) A Srivastava Hypergeometric Function”, Math. Sci. Appl. E-Notes, vol. 6, no. 2, pp. 1–9, Oct. 2018, [Online]. Available: https://izlik.org/JA33NY27LC

ISNAD

Şahin, Recep - Yağcı, Oğuz. “H_A^(τ_1,τ_2,τ_3 ) A Srivastava Hypergeometric Function”. Mathematical Sciences and Applications E-Notes 6/2 (October 1, 2018): 1-9. https://izlik.org/JA33NY27LC.

JAMA

1.Şahin R, Yağcı O. H_A^(τ_1,τ_2,τ_3 ) A Srivastava Hypergeometric Function. Math. Sci. Appl. E-Notes. 2018;6:1–9.

MLA

Şahin, Recep, and Oğuz Yağcı. “H_A^(τ_1,τ_2,τ_3 ) A Srivastava Hypergeometric Function”. Mathematical Sciences and Applications E-Notes, vol. 6, no. 2, Oct. 2018, pp. 1-9, https://izlik.org/JA33NY27LC.

Vancouver

1.Recep Şahin, Oğuz Yağcı. H_A^(τ_1,τ_2,τ_3 ) A Srivastava Hypergeometric Function. Math. Sci. Appl. E-Notes [Internet]. 2018 Oct. 1;6(2):1-9. Available from: https://izlik.org/JA33NY27LC