Expression for restricted partition function through Bernoulli polynomials

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.