Probabilistic derivation of some generating functions for the Laguerre polynomials

Computers and Mathematics with Applications

Volumn 38, Issue 7, 1999, Pages 21-29

  Lee, Poh Aun ^a   Ong, Seng Huat ^b   Srivastava, H M ^c  

^a MULTIMEDIA UNIVERSITY   (Malaysia)

^b UNIVERSITY OF MALAYA   (Malaysia)

^c UNIVERSITY OF VICTORIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; GEOMETRY; INTEGRAL EQUATIONS; MATHEMATICAL TRANSFORMATIONS; NUMERICAL METHODS; POISSON DISTRIBUTION; POLYNOMIALS;

BILINEAR GENERATING FUNCTIONS; GENERATING FUNCTIONS; GROUP THEORETIC METHOD; HYPERGEOMETRIC FUNCTION; LAGUERRE POLYNOMIALS; NONCENTRAL NEGATIVE BINOMIAL DISTRIBUTION; PROBABILITY GENERATING FUNCTION; PROBABILITY MASS FUNCTION;

PROBABILITY;

EID: 0033204335     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(99)00234-5     Document Type: Article

References (15)

1. G. Szegö, Orthogonal polynomials, American Mathematical Society Colloquium Publications, Vol. 23, Fourth Edition, American Mathematical Society, Providence, RI, (1975).
2. H.M. Srivastava and H.L. Manocha, A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, (1984).
3. P.-A. Lee, Probability distribution and a generating function of Laguerre polynomials, Bull. Inst. Math. Acad. Sinica 25, 151-154, (1997).
4. S.-H. Ong and P.-A. Lee, The non-central negative binomial distribution, Biometrical J. 21, 611-627, (1979).
5. A. Erdélyi, Transformation of a certain series of products of confluent hypergeometric functions: Applications to Laguerre and Charlier polynomials, Compositio Math. 7, 340-352, (1939).
6. H. Buchholz, The confluent hypergeometric function with special emphasis on its applications, (Translated from the German by H. Lichtblau and K. Wetzel), Springer Tracts in Natural Philosophy, Vol. 15, Springer-Verlag, New York, (1969).
7. E.R. Hansen, A Table of Series and Products, Prentice-Hall, Englewood Cliffs, NJ, (1975).
8. S.K. Chatterjea, Group-theoretic origins of certain generating functions of Laguerre polynomials, Bull. Inst. Math. Acad. Sinica 3, 369-375, (1975).
9. W. Miller, Jr., Lie Theory and Special Functions, Academic Press, New York, (1968).
10. E.B. McBride, Obtaining Generating Functions, Springer Tracts in Natural Philosophy, Vol. 21, Springer-Verlag, New York, (1971).
11. J.H. Hubbell and H.M. Srivastava, Certain theorems on bilateral generating functions involving Hermite, Laguerre, and Gegenbauer polynomials, J. Math. Anal. Appl. 152, 343-353, (1990).
12. Th.M. Rassias and H.M. Srivastava, Some general families of generating functions for the Laguerre polynomials, J. Math. Anal. Appl. 174, 528-538, (1993).
13. L.A. Lyusternik, New work in the probabilistic theory of special functions, Russian Math. Surveys 33 (3), 55-96, (1978).
14. J.M. Dickey, Multiple hypergeometric functions: Probabilistic interpretations and statistical uses, J. Amer. Statist. Assoc. 78, 628-637, (1983).
15. N.L. Johnson, S. Kotz and A.W. Kemp, Univariate Discrete Distributions, Second Edition, John Wiley and Sons, New York, (1992).