Rainville polynomials

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

$e^w{I}_0(zw)=\sum _n{p}_n(z)w^n$

(Boas Buck).

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, ISBN 978-0-387-03123-1, https://books.google.com/books?id=eihMuwkh4DsC 
• 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