Pidduck polynomials

In mathematics, the Pidduck polynomials s_n(x) are polynomials introduced by Pidduck (1910, 1912) given by the generating function

\displaystyle \sum _{n}{\frac {s_{n}(x)}{n!}}t^{n}=\left({\frac {1+t}{1-t}}\right)^{x}(1-t)^{{-1}}

References

Boas, Ralph P.; Buck, R. Creighton (1958), Polynomial expansions of analytic functions, Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge., 19, Berlin, New York: Springer-Verlag, MR 0094466
Pidduck, F. B. (1910), "On the Propagation of a Disturbance in a Fluid under Gravity", Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, The Royal Society, 83 (563): 347–356, doi:10.1098/rspa.1910.0023, ISSN 0950-1207, JSTOR 92977
Pidduck, F. B. (1912), "The Wave-Problem of Cauchy and Poisson for Finite Depth and Slightly Compressible Fluid", Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, The Royal Society, 86 (588): 396–405, doi:10.1098/rspa.1912.0031, ISSN 0950-1207, JSTOR 93103
Roman, Steven (1984), The umbral calculus, Pure and Applied Mathematics, 111, London: Academic Press Inc. [Harcourt Brace Jovanovich Publishers], ISBN 978-0-12-594380-2, MR 0741185 Reprinted by Dover, 2005

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