Faulhaber's theorem on power sums
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Publication:1025909
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
alternating sumBernoulli polynomialpower sumEuler polynomial\(r\)-fold alternating power sum\(r\)-fold power sumFaulhaber's theorem
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)
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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
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