Some families of hypergeometric polynomials and associated integral representations

Journal of Mathematical Analysis and Applications

Volumn 294, Issue 2, 2004, Pages 399-411

  Lin, Shy Der ^a   Chao, Yi Shan ^a   Srivastava, H M ^b  

^a CHUNG YUAN CHRISTIAN UNIVERSITY   (Taiwan)

^b UNIVERSITY OF VICTORIA   (Canada)

Author keywords

Bessel polynomials; Eulerian beta integral; Gamma function; Gould Hopper polynomials; Hermite polynomials; Hypergeometric functions; Hypergeometric polynomials; Integral representations; Jacobi polynomials; Konhauser Toscano polynomials; Laguerre polynomials; Linearization relationship

Indexed keywords

EID: 3142777042     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2004.01.024     Document Type: Article

References (18)

1. Carlitz L. An integral for the product of two Laguerre polynomials Boll. Un. Mat. Ital. (3) 17 1962 25-28
2. Chatterjea S.K. An integral representation for the product of two generalized Bessel polynomials Boll. Un. Mat. Ital. (3) 18 1963 377-381
3. Chatterjea S.K. Integral representation for the product of two Jacobi polynomials J. London Math. Soc. 39 1964 753-756
4. Erdélyi A. Magnus W. Oberhettinger F. Tricomi F.G. Higher Transcendental Functions, vol. I 1953 McGraw-Hill New York
5. González B. Matera J. Srivastava H.M. Some q-generating functions and associated generalized hypergeometric polynomials Math. Comput. Modelling 34 1/2 2001 133-175
6. Gould H.W. Hopper A.T. Operational formulas connected with two generalizations of Hermite polynomials Duke Math. J. 29 1962 51-63
7. Konhauser J.D.E. Biorthogonal polynomials suggested by the Laguerre polynomials Pacific J. Math. 21 1967 303-314
8. Krall H.L. Frink O. A new class of orthogonal polynomials: The Bessel polynomials Trans. Amer. Math. Soc. 65 1949 100-115
9. Lin S.-D. Srivastava H.M. Wang P.-Y. Some families of hypergeometric transformations and generating relations Math. Comput. Modelling 36 2002 445-459
10. Magnus W. Oberhettinger F. Soni R.P. Formulas and Theorems for the Special Functions of Mathematical Physics, Third enlarged ed. 1966 Springer-Verlag New York
11. Srivastava H.M. A contour integral involving Fox's H-function Indian J. Math. 14 1972 1-6
12. Srivastava H.M. A note on the integral representation for the product of two generalized Rice polynomials Collect. Math. 24 1973 117-121
13. Srivastava H.M. Joshi C.M. Integral representation for the product of a class of generalized hypergeometric polynomials Acad. Roy. Belg. Bull. Cl. Sci. (5) 60 1974 919-926
14. Srivastava H.M. Manocha H.L. A Treatise on Generating Functions 1984 Halsted/Ellis Horwood/Wiley New York/Chichester/New York
15. Srivastava H.M. Panda R. An integral representation for the product of two Jacobi polynomials J. London Math. Soc. (2) 12 1976 419-425
16. Szegö G. Orthogonal Polynomials, Fourth ed. American Mathematical Society Colloquium Publications vol. 23 1975 American Mathematical Society Providence, RI
17. Toscano L. Una generalizzazione dei polinomi di Laguerre Giorn. Mat. Battaglini (5) 4 1956 123-138
18. Whittaker E.T. Watson G.N. A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; with an Account of the Principal Transcendental Functions Fourth ed. 1927 Cambridge Univ. Press Cambridge