, Volume 15, Issue 2, pp 177-185
Date: 08 Feb 2008

Expression for restricted partition function through Bernoulli polynomials

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Abstract

Explicit expressions for restricted partition function W(s,d m ) and its quasiperiodic components W j (s,d m ) (called Sylvester waves) for a set of positive integers d m ={d 1,d 2,…,d m } are derived. The formulas are represented in a form of a finite sum over Bernoulli polynomials of higher order with periodic coefficients.