CERTAIN SEQUENCE OF FUNCTIONS INVOLVING GENERALIZED HYPERGEOMETRIC FUNCTIONS

Yıl 2015, Cilt: 3 Sayı: 2, 45 - 53, 30.10.2015

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

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

Cited By: 2

Öz

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.

Anahtar Kelimeler

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

Kaynakça

• [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.