CERTAIN SEQUENCE OF FUNCTIONS INVOLVING GENERALIZED HYPERGEOMETRIC FUNCTIONS

P. Agarwal; S. Jaın; İ. O. Kıymaz; M. Chand; S.k.q. Al-omarı

doi:10.36753/mathenot.421329

EN

CERTAIN SEQUENCE OF FUNCTIONS INVOLVING GENERALIZED HYPERGEOMETRIC FUNCTIONS

Abstract

A remarkably large number of operational techniques have drawn the attention of several researchers in the study of sequence of functions and polynomials. In this sequel, here, we aim to introduce a new sequence of functions involving the generalized Gauss hypergeometric function by using operational techniques. Some generating relations and finite summation formula of the sequence presented here are also considered.

Keywords

Special function,generating relations,generalized Gauss hypergeomtric functions,Sequence of function,finite summation formula

References

[1] Agarwal, P., Chand, M., (2013), On new sequence of functions involving pFq, South Asian Journal of Mathematics , Vol. 3 ( 3 ) : 199-210.
[2] Agarwal, P., Chand, M., (2013), A new sequence of functions involving pjFqj , MathematicalSciences And Applications E-Notes, Volume 1 No. 2 pp. 173-190.
[3] Agarwal, P., Chand, M.,(2013), Graphical Interpretation of the New Sequence of Functions Involving Mittage-Leffler Function Using Matlab, American Journal of Mathematics and Statistics 2013, 3(2): 73-83 DOI: 10.5923/j.ajms.20130302.02.
[4] Agarwal, P., Chand, M. and Dwivedi, S.,(2014), A Study on New Sequence of Functions Involving H-Function, American Journal of Applied Mathematics and Statistics, Vol. 2, No. ¯ 1, 34-39.
[5] Chak, A. M., (1956) A class of polynomials and generalization of stirling numbers, Duke J. Math., 23, 45-55.
[6] Chandel, R.C.S., (1973) A new class of polynomials, Indian J. Math., 15(1), 41-49.
[7] Chandel, R.C.S., (1974) A further note on the class of polynomials T α,kn (x, r, p), Indian J.Math.,16(1), 39-48.
[8] Chatterjea, S. K., (1964) On generalization of Laguerre polynomials, Rend. Mat. Univ. Padova, 34, 180-190.
[9] Gould, H. W. and Hopper, A. T., (1962) Operational formulas connected with two generalizations of Hermite polynomials, Duck Math. J., 29, 51-63.
[10] Joshi, C. M. and Prajapat, M. L., (1975) The operator Ta,k, and a generalization of certain classical polynomials, Kyungpook Math. J., 15, 191-199.

[11] Mittal, H. B., (1971) A generalization of Laguerre polynomial, Publ. Math. Debrecen, 18, 53-58.
[12] Mittal, H. B., (1971) Operational representations for the generalized Laguerre polynomial, Glasnik Mat.Ser III, 26(6), 45-53.
[13] Mittal, H. B., (1977) Bilinear and Bilateral generating relations, American J. Math., 99, 23-45.
[14] O¨zergin, E., Some properties of hypergeometric functions,Ph.D. Thesis, Eastern Mediterranean University, North Cyprus, February 2011.
[15] Patil, K. R. and Thakare, N. K., (1975) Operational formulas for a function defined by a generalized Rodrigues formula-II, Sci. J. Shivaji Univ. 15, 1-10.
[16] Shrivastava, P. N., (1974) Some operational formulas and generalized generating function, The Math. Education, 8, 19-22.
[17] Shukla, A. K. and Prajapati J. C., (2007) On some properties of a class of Polynomials suggested by Mittal, Proyecciones J. Math., 26(2), 145-156.
[18] Srivastava, H. M. and Choi,J., (2012) Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers, Amsterdam, London and New York.
[19] Srivastava, A. N. and Singh, S. N., (1979) Some generating relations connected with a function defined by a Generalized Rodrigues formula, Indian J. Pure Appl. Math., 10(10), 1312-1317.
[20] Srivastava, H. M. and Singh, J. P., (1971) A class of polynomials defined by generalized, Rodrigues formula, Ann. Mat. Pura Appl., 90(4), 75-85.
[21] Wright, E.M., (1935a) The asymptotic expansion of the generalized hypergeometric function. J. London Math. Soc. 10. 286-293.
[22] E.Özergin, Some properties of hypergeometric functions,Ph.D. Thesis, Eastern Mediterranean University, North Cyprus, February 2011.
[23] E. Özergin, M. A. O¨zarslan and A. Altin, Extension of gamma, beta and hypergeometric functions, J. Comput. Appl. Math. 235(2011), 4601-4610.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

P. Agarwal

S. Jaın This is me

İ. O. Kıymaz This is me

M. Chand This is me

S.k.q. Al-omarı

Publication Date

October 30, 2015

Submission Date

August 13, 2015

Acceptance Date

-

Published in Issue

Year 2015 Volume: 3 Number: 2

DOI

https://doi.org/10.36753/mathenot.421329

IZ

https://izlik.org/JA57AL75UL

APA

Agarwal, P., Jaın, S., Kıymaz, İ. O., Chand, M., & Al-omarı, S. (2015). CERTAIN SEQUENCE OF FUNCTIONS INVOLVING GENERALIZED HYPERGEOMETRIC FUNCTIONS. Mathematical Sciences and Applications E-Notes, 3(2), 45-53. https://doi.org/10.36753/mathenot.421329

AMA

1.Agarwal P, Jaın S, Kıymaz İO, Chand M, Al-omarı S. CERTAIN SEQUENCE OF FUNCTIONS INVOLVING GENERALIZED HYPERGEOMETRIC FUNCTIONS. Math. Sci. Appl. E-Notes. 2015;3(2):45-53. doi:10.36753/mathenot.421329

Chicago

Agarwal, P., S. Jaın, İ. O. Kıymaz, M. Chand, and S.k.q. Al-omarı. 2015. “CERTAIN SEQUENCE OF FUNCTIONS INVOLVING GENERALIZED HYPERGEOMETRIC FUNCTIONS”. Mathematical Sciences and Applications E-Notes 3 (2): 45-53. https://doi.org/10.36753/mathenot.421329.

EndNote

Agarwal P, Jaın S, Kıymaz İO, Chand M, Al-omarı S (October 1, 2015) CERTAIN SEQUENCE OF FUNCTIONS INVOLVING GENERALIZED HYPERGEOMETRIC FUNCTIONS. Mathematical Sciences and Applications E-Notes 3 2 45–53.

IEEE

[1]P. Agarwal, S. Jaın, İ. O. Kıymaz, M. Chand, and S. Al-omarı, “CERTAIN SEQUENCE OF FUNCTIONS INVOLVING GENERALIZED HYPERGEOMETRIC FUNCTIONS”, Math. Sci. Appl. E-Notes, vol. 3, no. 2, pp. 45–53, Oct. 2015, doi: 10.36753/mathenot.421329.

ISNAD

Agarwal, P. - Jaın, S. - Kıymaz, İ. O. - Chand, M. - Al-omarı, S.k.q. “CERTAIN SEQUENCE OF FUNCTIONS INVOLVING GENERALIZED HYPERGEOMETRIC FUNCTIONS”. Mathematical Sciences and Applications E-Notes 3/2 (October 1, 2015): 45-53. https://doi.org/10.36753/mathenot.421329.

JAMA

1.Agarwal P, Jaın S, Kıymaz İO, Chand M, Al-omarı S. CERTAIN SEQUENCE OF FUNCTIONS INVOLVING GENERALIZED HYPERGEOMETRIC FUNCTIONS. Math. Sci. Appl. E-Notes. 2015;3:45–53.

MLA

Agarwal, P., et al. “CERTAIN SEQUENCE OF FUNCTIONS INVOLVING GENERALIZED HYPERGEOMETRIC FUNCTIONS”. Mathematical Sciences and Applications E-Notes, vol. 3, no. 2, Oct. 2015, pp. 45-53, doi:10.36753/mathenot.421329.

Vancouver

1.P. Agarwal, S. Jaın, İ. O. Kıymaz, M. Chand, S.k.q. Al-omarı. CERTAIN SEQUENCE OF FUNCTIONS INVOLVING GENERALIZED HYPERGEOMETRIC FUNCTIONS. Math. Sci. Appl. E-Notes. 2015 Oct. 1;3(2):45-53. doi:10.36753/mathenot.421329