Gottlieb polynomials

In mathematics, Gottlieb polynomials are a family of discrete orthogonal polynomials given by

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

Further reading

• Rainville, Earl D. (1960), Special functions, New York: The Macmillan Co., MR 0107725