Meixner polynomials

Summary

The Meixner polynomials $M_n(x; \beta, c)$ are the orthogonal polynomials of the negative binomial (Pascal) distribution on the nonnegative integers. They are a discrete analogue of the Laguerre polynomials, which arise from them in a limit. They sit in the Askey scheme at the level of the ${}_2F_1$ series, together with the Jacobi and Krawtchouk polynomials.