Abstract
This paper gives a new expansion formula which essentially involves a double sum. As a consequence of our main result, eq. (6), various types of generating relations are seen to emerge and relevance with some known results is pointed out briefly. The usefulness of our main result is also indicated by considering its application to a probabilistic method for a lattice path enumeration problem.
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References
Carlitz L, A class of generating functions,SIAM J. Math. Anal. 8 (1977) 518–532
Exton H,Multiple hypergeometric functions and applications, (Chicester: Ellis Horwood Ltd) 1976
Gessel I M, A probabilistic method for lattice path enumeretion,J. stat. Planning and Inference 14 (1986) 49–58
Gould H W, A series transformation for finding convolution identities,Duke Math. J. 28 (1961) 193–202
Raina R K, On certain generating relations,Math. Japan. 27 (1982) 591–595
Raina R K, Extension of certain classes of generating functions,Rend. Seminar. Mat. Univ. Padova 81 (1989) 1–7
Srivastava H M, Some generalizations of Carlitz's theorem,Pacific J. Math 85 (1979) 471–477
Srivastava H M and Manocha H L,A treatise on generating functions, (Chicester: Ellis Horwood Ltd.) 1984
Srivastava H M and Raina R K, New generating functions for certain polynomial systems associated with the H-functions,Hokkaido Math. J. 10 (1981) 34–45
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Raina, R.K. Extension of certain types of generating relations. Proc. Indian Acad. Sci. (Math. Sci.) 100, 133–136 (1990). https://doi.org/10.1007/BF02880957
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DOI: https://doi.org/10.1007/BF02880957