Note on two extensions of the classical formula for sums of powers on arithmetic progressions

DOI10.1186/S13662-017-1250-YzbMath1444.05018OpenAlexW2729821045WikidataQ59603294 ScholiaQ59603294MaRDI QIDQ1726210

José A. Adell, Alberto Lekuona

Publication date: 19 February 2019

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13662-017-1250-y

zbMATH Keywords

Bernoulli polynomialsbinomial mixtureforward differencebinomial transformsum of powers formula

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Combinatorial identities, bijective combinatorics (05A19) Binomial coefficients; factorials; (q)-identities (11B65)

Related Items (2)

A Kirchhoff-type problem involving concave-convex nonlinearities ⋮ A probabilistic generalization of the Stirling numbers of the second kind

Cites Work

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• Symmetric recurrence relations and binomial transforms
• On differences of zeta values
• Signed binomial approximation of binomial mixtures via differential calculus for linear opera\-tors
• Finding sum of powers on arithmetic progressions with application of Cauchy's equation
• Generalizations of Euler numbers and polynomials
• Combinatorial sums and finite differences
• A \(q\)-analogue of Faulhaber's formula for sums of powers
• Iterating the Cesàro operators
• Rates of convergence for the iterates of Cesàro operators

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