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

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

References

1. Gottlieb, M. J. (1938). "Concerning some polynomials orthogonal on a finite or enumerable set of points". American Journal of Mathematics. 60 (2): 453–458. doi:10.2307/2371307. ISSN 0002-9327. JFM 64.0329.01. JSTOR 2371307.

Further reading

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

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