Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



Generating functions for relatives of classical polynomials

Authors: P. D. Barry and D. J. Hurley
Journal: Proc. Amer. Math. Soc. 103 (1988), 839-846
MSC: Primary 33A99; Secondary 05A15
MathSciNet review: 947668
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For several classical polynomials $ {u_n}(x)$ satisfying a second order linear differential equation $ {D_n}(x)$, there is a generating function $ u(x,t) = \sum\nolimits_{n = 0}^\infty {{u_n}(x){t^n}} $. We provide expansions $ \upsilon (x,t) = \sum\nolimits_{n = 0}^\infty {{\upsilon _n}(x){t^n}} $ where $ {\upsilon _n}(x)$ is a second solution of $ {D_n}(x)$.

References [Enhancements On Off] (What's this?)

  • [1] M. Abramowitz and I. A. Stegun, Handbook of mathematical functions, Dover, New York, 1965.
  • [2] A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher transcendental functions, vol. III, McGraw-Hill, New York, 1955. MR 0066496 (16:586c)
  • [3] E. B. McBride, Obtaining generating functions, Springer-Verlag, Berlin and New York, 1971. MR 0279355 (43:5077)
  • [4] H. M. Srivastava and H. L. Manocha, A treatise on generating functions, Ellis Horwood and Wiley, New York, 1984. MR 750112 (85m:33016)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 33A99, 05A15

Retrieve articles in all journals with MSC: 33A99, 05A15

Additional Information

Keywords: Generating functions, classical polynomials, orthogonal polynomials
Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society