Gottlieb polynomials

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

$\displaystyle \ell_n(x,\lambda) = e^{-n\lambda}\sum_k(1-e^\lambda)^k\binom{n}{k}\binom{x}{k} =e^{-n\lambda}{}_2F_1(-n,-x;1;1-e^\lambda)$

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