A new result for hypergeometric polynomials
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- by Kung-Yu Chen and H. M. Srivastava PDF
- Proc. Amer. Math. Soc. 133 (2005), 3295-3302 Request permission
Abstract:
In some recent investigations involving differential operators for generalized Laguerre polynomials, Herman Bavinck (1996) encountered and proved a certain summation formula for the classical Laguerre polynomials. The main object of this sequel to Bavinck’s work is to prove a generalization of this summation formula for a class of hypergeometric polynomials. The demonstration, which is presented here in the general case, differs markedly from the earlier proof given for the known special case. The general summation formula is also applied to derive the corresponding result for the classical Jacobi polynomials.References
- H. Bavinck, A new result for Laguerre polynomials, J. Phys. A 29 (1996), no. 11, L277–L279. MR 1399252, DOI 10.1088/0305-4470/29/11/001
- H. M. Srivastava, Some families of generating functions associated with the Stirling numbers of the second kind, J. Math. Anal. Appl. 251 (2000), no. 2, 752–769. MR 1794769, DOI 10.1006/jmaa.2000.7049
- H. M. Srivastava and H. L. Manocha, A treatise on generating functions, Ellis Horwood Series: Mathematics and its Applications, Ellis Horwood Ltd., Chichester; Halsted Press [John Wiley & Sons, Inc.], New York, 1984. MR 750112
Additional Information
- Kung-Yu Chen
- Affiliation: Department of Mathematics, Tamkang University, Tamsui 25137, Taiwan, Republic of China
- Email: kychen@math.tku.edu.tw
- H. M. Srivastava
- Affiliation: Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3P4, Canada
- Email: harimsri@math.uvic.ca
- Received by editor(s): February 26, 2004
- Received by editor(s) in revised form: June 15, 2004
- Published electronically: May 4, 2005
- Communicated by: Carmen C. Chicone
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 3295-3302
- MSC (2000): Primary 33C05, 33C45; Secondary 11B73
- DOI: https://doi.org/10.1090/S0002-9939-05-07895-0
- MathSciNet review: 2161152