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In mathematics, the Rainville polynomials \( p_n(z) \) are polynomials introduced by Rainville (1945) given by the generating function

\( \displaystyle e^wI_0(zw) = \sum_np_n(z)w^n \)

Boas & Buck (1958, p.46).


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
Rainville, Earl D. (1945), "Notes on Legendre polynomials", Bulletin of the American Mathematical Society 51: 268–271, doi:10.1090/S0002-9904-1945-08330-X, ISSN 0002-9904, MR 0011750

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