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

${\displaystyle \displaystyle e^{w}I_{0}(zw)=\sum _{n}p_{n}(z)w^{n}}$

Boas & Buck (1958, p.46).

References

• 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, ISBN 978-0-387-03123-1, MR 0094466
• Rainville, Earl D. (1945), "Notes on Legendre polynomials", Bulletin of the American Mathematical Society, 51 (4): 268–271, doi:10.1090/S0002-9904-1945-08330-X, ISSN 0002-9904, MR 0011750

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