Gottlieb polynomials explained

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

\displaystyle\elln(x,λ)=e-nλ

λ)
\sum
k(1-e

k\binom{n}{k}\binom{x}{k}=e-nλ{}2F

λ)
1(-n,-x;1;1-e

[1]

Notes and References

  1. Gottlieb . M. J. . 1938 . Concerning some polynomials orthogonal on a finite or enumerable set of points. . . 0002-9327 . 60 . 2 . 453–458 . 10.2307/2371307 . 64.0329.01 . 2371307 .