Mott polynomials


In mathematics the Mott polynomials sn are polynomials given by the exponential generating function:

Introduction

They were introduced by Nevill Francis Mott who applied them to a problem in the theory of electrons.

Logic

Because the factor in the exponential has the power series
in terms of Catalan numbers, the coefficient in front of of the polynomial can be written as
By differentiation the recurrence for the first derivative becomes
The first few of them are

Sheffer sequence

The polynomials sn form the associated Sheffer sequence for –2t/

Generalized hypergeometric function

An explicit expression for them in terms of the generalized hypergeometric function 3F0: