A two-sided Faulhaber-like formula involving Bernoulli polynomials

Abstract

We give a new identity involving Bernoulli polynomials and combinatorial numbers. This provides, in particular, a Faulhaber-like formula for sums of the form $1^m(n-1{)}^m+2^m(n-2{)}^m+\cdots +(n-1{)}^m{1}^m$ for positive integers $m$ and $n$.

arXiv comment5 pages

References in corpus (1)

• On the distribution of the eigenvalues of the area operator in loop quantum gravity

Cited by in corpus (1)

• A Generalized Faulhaber Inequality, Improved Bracketing Covers, and Applications to Discrepancy