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A simple recursion for power sum polynomials

Author(s) -

Helmut Länger

Publication year - 2014

Publication title -

elemente der mathematik

Language(s) - English

Resource type - Journals

eISSN - 1420-8962

pISSN - 0013-6018

DOI - 10.4171/em/249

Subject(s) - simple (philosophy) , recursion (computer science) , mathematics , double recursion , sums of powers , power (physics) , algebra over a field , calculus (dental) , pure mathematics , discrete mathematics , algorithm , physics , medicine , philosophy , dentistry , epistemology , quantum mechanics

There exists some literature on power sum polynomials and their connection to Bernoulli numbers and Bernoulli polynomials (cf., e.g., [1]–[5]). In this note we provide an elementary proof of a simple recursion for power sum polynomials. In the followingN (N0 resp.R) denote the set of all positive integers (non-negative integers resp. real numbers), let k ∈ N, n ∈ N0 and x ∈ R and put Pk(n) := n ∑

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