Pidduck polynomials

In mathematics, the Pidduck polynomialss_n(x) are polynomials introduced by Pidduck ^{[1] [2]} given by the generating function

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

^{[3] [4]}

See also

• Umbral calculus

References

1. 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, 83 (563), The Royal Society: 347–356, Bibcode:1910RSPSA..83..347P, doi: 10.1098/rspa.1910.0023 , ISSN   0950-1207, JSTOR   92977
2. 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, 86 (588), The Royal Society: 396–405, Bibcode:1912RSPSA..86..396P, doi: 10.1098/rspa.1912.0031 , ISSN   0950-1207, JSTOR   93103
3. Boas, Ralph P.; Buck, R. Creighton (1958), Polynomial expansions of analytic functions, Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge., vol. 19, Berlin, New York: Springer-Verlag, p. 38, ISBN   978-0-387-03123-1, MR   0094466
4. Roman, Steven (1984), The umbral calculus, Pure and Applied Mathematics, vol. 111, London: Academic Press Inc. [Harcourt Brace Jovanovich Publishers], ISBN   978-0-12-594380-2, MR   0741185