A NEW SEQUENCE OF FUNCTIONS INVOLVING (p_j ) F_(q_j )

Year 2013, Volume: 1 Issue: 2, 173 - 190, 01.12.2013

Praveen Agarwal Meharchand

Abstract

A remarkably large number of operational techniques have drawnthe attention of several researchers in the study of sequences of functions andpolynomials. Very recently, Agarwal and Chand gave a interesting new sequence of functions involving thepFq.Using the same method, in this paper,we present a new sequence of functions involving product of thepFq. Somegenerating relations and finite summation formula of the sequence presentedhere are also considered. In the last, we use Matlab (R2012a) for each parameter of our main sequence, which gives the eccentric characteristics in the areaof sequences of functions or class of polynomials

Keywords

Special function , generating relations , gaussian hypergeomtric functions , sequence of function , finite summation formula , symbolic representation

References

• Agarwal, P. and Chand, M., On new sequence of functions involvingpFq, South Asian Journal of Mathematics, Vol. 3 (2013), no.3, 199-210.
• Chak, A. M., A class of polynomials and generalization of stirling numbers, Duke J. Math., 23 (1956), 45-55.
• Chandel, R. C. S., A new class of polynomials, Indian J. Math., 15 (1973), no.1, 41-49.
• Chandel, R. C. S., A further note on the class of polynomials Tα,k(x, r, p), Indian J. Math.,16 n
• (1974), no. 1, 39-48.
• Chatterjea, S. K., On generalization of Laguerre polynomials, Rend. Mat. Univ. Padova, 34 (1964), 180-190.
• Gould, H. W. and Hopper, A. T., Operational formulas connected with two generalizations of Hermite polynomials, Duke Math. J. 29 (1962), no. 1, 51-63.
• Joshi, C. M. and Prajapat, M. L., The operator Ta,kand a generalization of certain classical polynomials, Kyungpook Math. J. 15 (1975), 191-199.
• Mittal, H. B., A generalization of Laguerre polynomial, Publ. Math. Debrecen 18 (1971), 53-58. [9] Mittal, H. B., Operational representations for the generalized Laguerre polynomial, Glasnik Mat.Ser III 26 (1971), no. 6, 45-53.
• Mittal, H. B., Bilinear and Bilateral generating relations, American J. Math. 99 (1977), 23-45. [11] Patil, K. R. and Thakare, N. K., Operational formulas for a function defined by a generalized Rodrigues formula-II, Sci. J. Shivaji Univ. 15 (1975), 1-10.
• Prajapati, J. C. and Ajudia, N. K., On sequence of functions and their MATLAB implemen- tation, International Journal od Physical, Chemical and Mathematical Sciences (2012), no. 2, 24-34.
• Salembhai, I. A., Prajapti, J. C. and Shukla, A.K., On sequence of functions, Commun. Korean Math. 28 (2013), no.1, 123-134.
• Shrivastava, P. N., Some operational formulas and generalized generating function, The Math. Education 8 (1974), 19-22.
• Srivastava, H. M. and Choi, J., Zeta and q-Zeta Functions and Associated Series and Inte- grals, Elsevier Science Publishers, Amsterdam, London and New York, 2012.
• Shukla, A. K. and Prajapati J. C., On some properties of a class of Polynomials suggested by Mittal, Proyecciones J. Math. 26 (2007), no. 2, 145-156.
• Singh, R. P., On generalized Truesdell polynomials, Rivista de Mathematica 8 (1968), 345- 353.
• 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. 10 (1979), no. 10, 1312-1317.
• Srivastava, H. M. and Singh, J. P., A class of polynomials defined by generalized Rodrigues formula, Ann. Mat. Pura Appl. 90 (1971), no. 4, 75-85.
• Department of Mathematics, Anand International College of Engineering, Jaipur- 303012, India
• E-mail address: [e-mail]
• Department of Mathematics, Singhania University, Pacheri Bari-333515, India
• E-mail address: [e-mail]