Journal of Integer Sequences

Journal: Journal of Integer Sequences

University of Waterloo

1530-7638

Publications 1 - 3 of 3

The Generalization of Faulhaber' s Formula to Sums of Arbitrary Complex Powers
Schumacher, Raphael (2022)
Journal of Integer Sequences
In this paper we present a generalization of Faulhaber's formula to sums of arbitrary complex powers m is an element of C. These summation formulas for sums of the form Sigma(right perpendicularxleft perpendicular)(k=1) k(m) and Sigma(k =1) (n) k(m), where x is an element of R+ and n is an element of N, are based on a series acceleration involving Stirling numbers of the first kind. While it is well-known that the corresponding expressions obtained from the Euler-Maclaurin summation formula diverge, our summation formulas are all very rapidly convergent.
An extended version of faulhaber’s formula
Schumacher, Raphael (2016)
Journal of Integer Sequences
Congruent Number Elliptic Curves Related to Integral Solutions of m2 = n2 + nl + n2
Halbeisen, Lorenz; Hungerbühler, Norbert (2019)
Journal of Integer Sequences

Publications 1 - 3 of 3