Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-19T07:32:11.272Z Has data issue: false hasContentIssue false
  • English
  • Français

Some new results for the Lagrange polynomials in several variables

Published online by Cambridge University Press:  17 February 2009

Kung Yu Chen ,
Shouh Jung Liu  and
H. M. Srivastava
Kung Yu Chen
Affiliation:
department of Mathematics Tamkang University, Tamsui 25137 Taiwan Republic of China; email: [email protected] [email protected].
Shouh Jung Liu
Affiliation:
department of Mathematics Tamkang University, Tamsui 25137 Taiwan Republic of China; email: [email protected] [email protected].
H. M. Srivastava
Affiliation:
department of Mathematics and Statistics University of Victoria, Victoria British Columbia V8W 3P4 Canada, email: [email protected].
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In some recent investigations involving certain differential operators for a general family of Lagrange polynomials, Chan el al. encountered and proved a certain summation identity for the Lagrange polynomials in several variables. In the present paper, we derive some generalizations of this summation identity for the Chan-Chyan-Srivastava polynomials in several variables. We also discuss a number of interesting corollaries and consequences of our main results.

Keywords

Lagrange polynomialssummation identityChan-Chyan-Srivastava polynomialsdifferential operatorsgenerating functionsJacobi polynomialsStirling numbers of the second kindCauchy integral formulaLaguerre polynomials.
Type
Articles
Information
The ANZIAM Journal , Volume 49 , Issue 2 , October 2007 , pp. 243 - 258
Copyright
Copyright © Australian Mathematical Society 2007

References

[1] Chan, W. C. C., Chyan, C. J. and Srivastava, H. M., “The Lagrange polynomials in several variables”, Integral Transform Spec Fund. 12 (2001) 139–148.CrossRefGoogle Scholar
[2] Chen, K. Y. and Srivastava, H. M., “A new result for hypergeometric polynomials”, Proc Amer Math Soc. 133 (2005) 3295–3302.CrossRefGoogle Scholar
[3] rdeiyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G., Higher Transcendental Functions, Volume III (McGraw-Hill Book Company, New York, Toronto and London, 1955).Google Scholar
[4] Altin, A., Erkus, E., Tasdelen, F., “The q-Lagrange polynomials in several variables”, Taiwanese J Math. 10 (2006) 1131–1137.Google Scholar
[5] Erkus, E., and Altin, A., “A note on the Lagrange polynomials in several variables”, J Math Anal Appl. 310 (2005) 139–148.CrossRefGoogle Scholar
[6] Erkus, E. and Srivastava, H. M., “A unified presentation of some families of multivariable polynomials”, Integral Transform Spec Fund. 17 (2006) 315–320.Google Scholar
[7] Srivastava, H. M. and Manocha, H. L., A Treatise on Generating Functions (Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1984).Google Scholar
[8] Szego, G., Orthogonal Polynomials, Volume 23 of American Mathematical Society Colloquium Publications, fourth edition (American Mathematical Society, Providence, Rhode Island, 1975).Google Scholar
[9] Tbmescu, I., Problems in Combinatorics and Graph Theory, Wiley-Interscience Series in Discrete Mathematics, Translated from the Romanian by Melter, R. A. (A Wiley-Interscience Publication, John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1985).Google Scholar