A Study on New Sequence of Functions Involving -Function

Praveen Agarwal^1, , Mehar Chand² and Saket Dwivedi³

¹Department of Mathematics, Anand International College of Engineering, Jaipur, India

²Department of Mathematics, Fateh College for Women, RampuraPhul, Bathinda, India

³Department of Mathematics, Suresh Gyan Vihar University, Jaipur, India

Cite this paper

Praveen Agarwal, Mehar Chand and Saket Dwivedi. A Study on New Sequence of Functions Involving -Function. American Journal of Applied Mathematics and Statistics. 2014; 2(1):34-39. doi: 10.12691/AJAMS-2-1-6

Abstract

A remarkably large number of operational techniques have drawn the attention of several researchers in the study of sequence of functions and polynomials. Very recently, Agarwal and Chand gave certain new sequence of functions involving the special functions in their series of papers. In this sequel, here, we aim to introduce a new sequence of functions involving the Generalized Mellin-Barnes Type of Contour Integrals by using operational techniques. Some generating relations and finite summation formulae of the sequence presented here are also considered. These generating relations and finite summation formulae are unified in nature and act as key formulae from which, we can obtain as their special cases.

Keywords

Special function, generating relations, - function, sequence of functions

Copyright

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References

[1]	Agarwal, P., On multiple integral relations involving generalized Mellin-Barnes type of contour integral, Tamsui O xf. J. Math. Sci. 2011, 27(4), 449-462.
[2]	Agarwal, P. and Chand, M., On new sequence of functions involving pFq, South Asian J Math, 2013, 3(3), 199-210.
[3]	Agarwal, P. and Chand, M., 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.
[4]	Agarwal, P. and Chand, M., On new sequence of functions involving pFq, South Asian Journal of Mathematics 2013 , Vol. 3 ( 3 ) : 199-210.
[5]	Agarwal, P. and Jain, S., On unified finite integrals involving a multivariable polynomial and a generalized Mellin Barnes type of contour integral having general argument, Nat. Acad. Sci. Lett. 2009, 32(9-10), 281-286.
[6]	Chak, A. M., A class of polynomials and generalization of stirling numbers, Duke J. Math. 1956, 23, 45-55.
[7]	Chandel, R.C.S., A new class of polynomials, Indian J. Math. 1973, 15(1), 41-49.
[8]	Chandel, R.C.S., A further note on the class of polynomials Tnα,k(x,r,p), Indian J. Math. 1974,16(1), 39-48.
[9]	Chatterjea, S. K., On generalization of Laguerre polynomials, Rend. Mat. Univ. Padova. 1964, 34, 180-190.
[10]	Gould, H. W. and Hopper, A. T., Operational formulas connected with two generalizations of Hermite polynomials, Duck Math. J. 1962, 29, 51-63.
[11]	Joshi, C. M. and Prajapat, M. L., The operator Ta,k, and a generalization of certain classical polynomials, Kyungpook Math. J. 1975, 15, 191-199.
[12]	K.C. Gupta and R.C. Soni, On a basic integral formula involving the product of the H-function and Fox H-function, J.Raj.Acad.Phy. Sci. 2006, 4 (3), 157-164.
[13]	K.C. Gupta, R. Jain and R. Agarwal, On existence conditions for a generalized Mellin-Barnes type integral Natl Acad Sci Lett. 2007, 30(5-6), 169-172.
[14]	Meijer, C.S., On the G-function, Proc. Nat. Acad. Wetensch 1946, 49, p. 227.
[15]	Mittal, H. B., A generalization of Laguerre polynomial, Publ. Math. Debrecen 1971, 18, 53-58.
[16]	Mittal, H. B., Operational representations for the generalized Laguerre polynomial, GlasnikMat.Ser III 1971, 26(6), 45-53.
[17]	Mittal, H. B., Bilinear and Bilateral generating relations, American J. Math. 1977, 99, 23-45.
[18]	Patil, K. R. and Thakare, N. K., Operational formulas for a function defined by a generalized Rodrigues formula-II, Sci. J. Shivaji Univ.1975, 15, 1-10.
[19]	Prajapati , J. C. and Ajudia, N. K., On New Sequence of Functions and Their MATLAB Computation International Journal of Physical, Chemical & Mathematical Sciences, 1(2),Accepted On: 27.08.2012.
[20]	Rathie, A.K., A new generalization of generalized hypergeometric functions, Le Mathematic he Fasc. II 1997, 52, 297-310.
[21]	Shrivastava, P. N., Some operational formulas and generalized generating function, The Math. Education 1974, 8, 19-22.
[22]	Shukla, A. K. and Prajapati J. C., On some properties of a class of Polynomials suggested by Mittal, Proyecciones J. Math.2007, 26(2), 145-156.
[23]	Singh, R. P., On generalized Truesdell polynomials, Rivista de Mathematica 1968, 8, 345-353.
[24]	Srivastava, A. N. and Singh, S. N., Some generating relations connected with a function defined by a Generalized Rodrigues formula, Indian J. Pure Appl. Math. 1979, 10(10), 1312-1317.
[25]	Srivastava, H.M., Gupta, K.C. and Goyal, S.P., The H-function of one and two variables with applications, South Asian Publishers, New Dehli, Madras ,1982.
[26]	Srivastava, H. M. and Singh, J. P., A class of polynomials defined by generalized, Rodrigues formula, Ann. Mat. Pura Appl. 1971, 90(4), 75-85.