Mott polynomials

In mathematics the Mott polynomials sn(x) are polynomials introduced by N. F. Mott (1932, p. 442) who applied them to a problem in the theory of electrons. They are given by

 exp(x((1-t^2)^{1/2}-1)/t) = \sum_ns_n(x)t^n/n!

The polynomials sn(x) form the associated Sheffer sequence for –2t/(1–t2) (Roman 1984, p.130). Arthur Erdélyi, Wilhelm Magnus, and Fritz Oberhettinger et al. (1955, p. 251) give an explicit expression for them in terms of the generalized hypergeometric function 3F0.

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