Journal: Journal of Integer Sequences
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University of Waterloo
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- The Generalization of Faulhaber' s Formula to Sums of Arbitrary Complex PowersItem type: Journal Article
Journal of Integer SequencesSchumacher, Raphael (2022)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 formulaItem type: Journal Article
Journal of Integer SequencesSchumacher, Raphael (2016) - Congruent Number Elliptic Curves Related to Integral Solutions of m2 = n2 + nl + n2Item type: Journal Article
Journal of Integer SequencesHalbeisen, Lorenz; Hungerbühler, Norbert (2019)
Publications 1 - 3 of 3