Bernoulli polynomials of the second kind
id:
bernoulli-polynomials-of-the-second-kind-223-2551981
title:
Bernoulli polynomials of the second kind
text:
The Bernoulli polynomials of the second kind ψn(x), also known as the Fontana–Bessel polynomials, are the polynomials defined by the following generating function: z x ln = ∑ n = 0 ∞ z n ψ n, | z | < 1. The first five polynomials are: ψ 0 = 1 ψ 1 = x + 1 2 ψ 2 = 1 2 x 2 − 1 12 ψ 3 = 1 6 x 3 − 1 4 x 2 + 1 24 ψ 4 = 1 24 x 4 − 1 6 x 3 + 1 6 x 2 − 19 720 Some authors define these polynomials slightly differently z x ln = ∑ n = 0 ∞ z n n! ψ n ∗, | z | < 1, so that ψ n ∗ = ψ n n! and may also use
brand slug:
wiki
category slug:
encyclopedia
description:
Polynomial sequence
original url:
https://en.wikipedia.org/wiki/Bernoulli_polynomials_of_the_second_kind
date created:
2018-09-26T03:18:22Z
date modified:
2024-09-14T03:47:45Z
main entity:
{"identifier":"Q60790776","url":"https://www.wikidata.org/entity/Q60790776"}
image:
fields total:
13
integrity:
15