Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A simple proof of Koornwinder’s addition formula for the little $q$-Legendre polynomials
HTML articles powered by AMS MathViewer

by Mizan Rahman PDF
Proc. Amer. Math. Soc. 107 (1989), 373-381 Request permission

Abstract:

Recently Koornwinder found an addition formula for the little $q$-Legendre polynomials by using Masuda et al.’s result that they are related to the matrix elements of the irreducible unitary representation of the twisted ${\text {SU(2)}}$ quantum group. Here we give an alternate derivation of the addition formula by using some summation and transformation formulas of basic hypergeometric series.
References
  • George E. Andrews and Richard Askey, Enumeration of partitions: the role of Eulerian series and $q$-orthogonal polynomials, Higher combinatorics (Proc. NATO Advanced Study Inst., Berlin, 1976) NATO Adv. Study Inst. Ser. C: Math. Phys. Sci., vol. 31, Reidel, Dordrecht-Boston, Mass., 1977, pp. 3–26. MR 519776
  • T. S. Chihara, An introduction to orthogonal polynomials, Mathematics and its Applications, Vol. 13, Gordon and Breach Science Publishers, New York-London-Paris, 1978. MR 0481884
  • George Gasper and Mizan Rahman, Basic hypergeometric series, 2nd ed., Encyclopedia of Mathematics and its Applications, vol. 96, Cambridge University Press, Cambridge, 2004. With a foreword by Richard Askey. MR 2128719, DOI 10.1017/CBO9780511526251
    • T. H. Koornwinder, The addition formula for little $q$-Legendre polynomials and the twisted ${\text {SU(2)}}$ quantum group, (to appear).
  • Tetsuya Masuda, Katsuhisa Mimachi, Yoshiomi Nakagami, Masatoshi Noumi, and Kimio Ueno, Representations of quantum groups and a $q$-analogue of orthogonal polynomials, C. R. Acad. Sci. Paris Sér. I Math. 307 (1988), no. 11, 559–564 (English, with French summary). MR 967361
  • S. L. Woronowicz, Compact matrix pseudogroups, Comm. Math. Phys. 111 (1987), no. 4, 613–665. MR 901157, DOI 10.1007/BF01219077
  • S. L. Woronowicz, Twisted $\textrm {SU}(2)$ group. An example of a noncommutative differential calculus, Publ. Res. Inst. Math. Sci. 23 (1987), no. 1, 117–181. MR 890482, DOI 10.2977/prims/1195176848
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 33D45, 33D80
  • Retrieve articles in all journals with MSC: 33D45, 33D80
Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 107 (1989), 373-381
  • MSC: Primary 33D45; Secondary 33D80
  • DOI: https://doi.org/10.1090/S0002-9939-1989-0979214-3
  • MathSciNet review: 979214