From Wikipedia, the free encyclopedia
In mathematics, the Rainville polynomials pn(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}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/11e78c77661c28ce4779f771d49a378b32c7e5d6)
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., 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