Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2018, 6(5), 136-147
DOI: 10.12691/tjant-6-5-3
Open AccessArticle

Some Hypergeometric Generating Relations Motivated by the Work of Srivastava and Their Generalizations

M.I. Qureshi1 and Sulakshana Bajaj2,

1Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia (A Central University), New Delhi - 110025, India,

2Department of Applied Sciences and Humanities, Modi Institute of Technology, Rawatbhata Road, Kota, Rajasthan 324010, India

Pub. Date: October 27, 2018

Cite this paper:
M.I. Qureshi and Sulakshana Bajaj. Some Hypergeometric Generating Relations Motivated by the Work of Srivastava and Their Generalizations. Turkish Journal of Analysis and Number Theory. 2018; 6(5):136-147. doi: 10.12691/tjant-6-5-3

Abstract

In the present paper, we have obtained hypergeometric generating relations associated with two hypergeometric polynomials of one variable and with their independent demonstrations via Gould's identity. As applications, some well known and new generating relations are deduced. Using bounded sequences, further generalizations of two main hypergeometric generating relations have also been given for two generalized polynomials and .

Keywords:
Jacobi Polynomials generalized Laguerre polynomial generalized Rice polynomial of Khandekar Gould's identity.

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References:

[1]  Whittaker, E. T. and Watson, G. N.; A Course of Modern Analysis, Fourth ed., Cambridge Univ. Press, Cambridge, London and New York (1927).
 
[2]  P´olya, G. and Szeg¨o, G; Problems and Theorems in Analysis, Vol. I, (Translated from theGerman by D.Aeppli) Springer-Verlag, New York, Heidelberg and Berlin (1972).
 
[3]  Gould, H. W.; Some generalizations of Vandermonde's Convolution, Amer. Math. Monthly, 63(1956); 84-91.
 
[4]  Riordan, J.; Combinatorial Identities, John Wiley & Sons, New York, London and Sydney (1968).
 
[5]  Srivastava, H. M. and Manocha, H. L.; A Treatise on Generating functions, Halsted Press (Ellis Horwood Ltd., Chichester, U. K.), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, (1984).
 
[6]  Rainville, E. D.; Special Functions, The Macmillan, New York, (1960); Reprinted by Chelsea Publishing Company, Bronx, New York, (1971).
 
[7]  Khandekar, P. R.; On a generalization of Rice's polynomial, I. Proc. Nat. Acad. Sci. India Sect. A, 34(1964); 157-162.
 
[8]  Srivastava, H. M.; A Note on Certain Generating functions for the Classical Polynomi-als, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8); 63(1977), 328-333.
 
[9]  Srivastava, H. M.; A class of Generating Functions for generalized Hypergeometric Poly-nomials (Abstract), Notices Amer. Math. Soc., 16(1969); 975 (Abstract #69T-B198).
 
[10]  Srivastava, H. M.; A class of Generating Functions for generalized Hypergeometric Poly-nomials, J. Math. Anal. Appl., 35 (1971); 230-235.
 
[11]  Srivastava, H. M.; Generating Functions for Jacobi and Laguerre Polynomials, Proc. Amer. Math. Soc., 23(1969); 590-595.
 
[12]  Brown, J. W.; New Generating Functions for Classical Polynomials, Proc. Amer. Math. Soc., 21(1969); 263-268.
 
[13]  Brown, J. W.; On Zero Type Sets of Laguerre Polynomials, Duke Math. J., 35(No.4) (1968); 821-823.
 
[14]  Carlitz, L.; Some Generating Functions for Laguerre Polynomials, Duke Math. J., 35(1968); 825-827.
 
[15]  Srivastava, H. M. and Singhal, J. P.; New Generating Functions for Jacobi and Related Polynomials, J. Math. Anal. Appl., 41 (1973); 748-752.
 
[16]  Calvez, L.-C. and G'enin, R. Sur les relations entre les fonctions g´en´eratrices et les for-mules de type Rodrigues, C. R. Acad. Sci. Paris S'er. A 269(1969); 651-654.
 
[17]  Milch, P. R.; A Probabilistic proof of a formula for Jacobi Polynomials by L. Carlitz, Proc. Cambridge Philos. Soc., 64(1968); 695-698.
 
[18]  Joshi, C. M. and Prajapat, M. L.; A Triple integral transformation and its applications to generating functions. Boll. Un. Mat. Ital. (5), 14A (1977); 264-274.
 
[19]  Karande, B. K. and Thakare, N. K.; Note on the generating function for generalized hy-pergeometric polynomials, Indian J. Pure Appl. Math., 6(1975); 1185-1187.