A refinement of Faulhaber's theorem concerning sums of powers of natural numbers

DOI10.1016/j.aml.2011.09.042zbMath1285.11034OpenAlexW2021342516MaRDI QIDQ427651

Ákos Pintér, Hari M. Srivastava, András Bazsó

Publication date: 14 June 2012

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2011.09.042

zbMATH Keywords

decompositionLaguerre polynomialsBernoulli polynomials and Bernoulli numbersFaulhaber's polynomialsring of polynomialssums of powers of natural numbers

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Bernoulli and Euler numbers and polynomials (11B68) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Polynomials in number theory (11C08)

Related Items (9)

Unnamed Item ⋮ Polynomial values of (alternating) power sums ⋮ A note on polynomial expressions for sums of power of integers multiplied by exponential terms ⋮ The denominators of power sums of arithmetic progressions ⋮ The linear algebra of ther-Whitney matrices ⋮ A generalization of power and alternating power sums to any Appell polynomials ⋮ Generalized Stirling numbers and sums of powers of arithmetic progressions ⋮ On the coefficients of power sums of arithmetic progressions ⋮ On alternating power sums of arithmetic progressions

Cites Work

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• Faulhaber's theorem on power sums
• Remarks on some relationships between the Bernoulli and Euler polynomials.
• Johann Faulhaber and Sums of Powers
• Fractional Calculus and the Sum of Powers of Natural Numbers
• Some formulas for the Bernoulli and Euler polynomials at rational arguments
• The Diophantine equation f(x) = g(y)

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