Gottlieb polynomials

In mathematics, Gottlieb polynomials are a family of discrete orthogonal polynomials introduced by Morris J. Gottlieb (1938). They are given by

\displaystyle \ell _{n}(x,\lambda )=e^{-n\lambda }\sum _{k}(1-e^{\lambda })^{k}{\binom {n}{k}}{\binom {x}{k}}=e^{-n\lambda }{}_{2}F_{1}(-n,-x;1;1-e^{\lambda })

References

Gottlieb, M. J. (1938), "Concerning some polynomials orthogonal on a finite or enumerable set of points.", American Journal of Mathematics, 60: 453–458, doi:10.2307/2371307, ISSN 0002-9327, JFM 64.0329.01
Rainville, Earl D. (1960), Special functions, New York: The Macmillan Co., MR 0107725

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.