The Generalization of Faulhaber's Formula to Sums of Arbitrary Complex Powers

zbMath1492.65007arXiv2103.08027MaRDI QIDQ5080342

Raphael Schumacher

Publication date: 31 May 2022

Full work available at URL: https://arxiv.org/abs/2103.08027

zbMATH Keywords

Bernoulli numberBernoulli polynomialStirling number of the first kindextended Faulhaber formulafinite Weniger transformationgeneralization of Faulhaber's formula

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Euler-Maclaurin formula in numerical analysis (65B15)

Uses Software

• DLMF
• OEIS

Cites Work

• Summation of divergent power series by means of factorial series
• The generalization of Faulhaber's formula to sums of non-integral powers
• The Cauchy numbers
• The special functions and their approximations. Vol. I, II
• Error bounds for the asymptotic expansion of the Hurwitz zeta function
• A note on inverse central factorial series
• Quantum calculus
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The Generalization of Faulhaber's Formula to Sums of Arbitrary Complex Powers