Faulhaber's theorem on power sums

DOI10.1016/j.disc.2008.07.027zbMath1220.11027arXivmath/0606090OpenAlexW1995985109MaRDI QIDQ1025909

Iris F. Zhang, Amy M. Fu, William Y. C. Chen

Publication date: 23 June 2009

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0606090

zbMATH Keywords

alternating sumBernoulli polynomialpower sumEuler polynomial\(r\)-fold alternating power sum\(r\)-fold power sumFaulhaber's theorem

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Binomial coefficients; factorials; (q)-identities (11B65) Bernoulli and Euler numbers and polynomials (11B68) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15)

Related Items

A treaty of symmetric function: An approach in deriving general formulation for sums of power for an arbitrary arithmetic progression Part 1, Applying Archimedes's method to alternating sums of powers, Summation formulas of \(q\)-hyperharmonic numbers, Summation formulas of hyperharmonic numbers with their generalizations, A refinement of Faulhaber's theorem concerning sums of powers of natural numbers, Euler sums of generalized alternating hyperharmonic numbers, A note on polynomial expressions for sums of power of integers multiplied by exponential terms, Generalized alternating hyperharmonic number sums with reciprocal binomial coefficients, Generalized hyperharmonic number sums with reciprocal binomial coefficients

Cites Work

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• Combinatorial interpretations of the \(q\)-Faulhaber and \(q\)-Salié coefficients
• Binomial determinants, paths, and hook length formulae
• A combinatorial proof of the sum of \(q\)-cubes
• On the {\(q\)}-analogue of the sum of cubes
• {\(q\)}-analogues of the sums of consecutive integers, squares, cubes, quarts and quints
• A new \(q\)-analogue of the sum of cubes
• A \(q\)-analogue of Faulhaber's formula for sums of powers
• Johann Faulhaber and Sums of Powers
• Elliptic Faulhaber polynomials and Lame densities of states
• A Quick Route to Sums of Powers
• Sums of Powers of Integers