In mathematics the Mott polynomials sn(x) are polynomials given by the exponential generating function: They were introduced by Nevill Francis Mott who applied them to a problem in the theory of electrons.
[1] 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 (sequence A137378 in the OEIS) The polynomials sn(x) form the associated Sheffer sequence for –2t/(1–t2)[2] An explicit expression for them in terms of the generalized hypergeometric function 3F0:[3]
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