An Explicit Formula for Restricted Partition Function through Bernoulli Polynomials

Details An Explicit Formula for Restricted Partition Function through Bernoulli Polynomials An Explicit Formula for Restricted Partition Function through Bernoulli Polynomials

2004-06-30

arxiv.org/abs/math/0407001v1

Mathematics

Number Theory

8 pages, submitted to The Ramanujan Journal

Scientific paper

Explicit expressions for restricted partition function $W(s,{\bf d}^m)$ and
its quasiperiodic components $W_j(s,{\bf d}^m)$ (called Sylvester waves) for a
set of positive integers ${\bf d}^m = \{d_1, d_2, ..., d_m\}$ are derived. The
formulas are represented in a form of a finite sum over Bernoulli polynomials
of higher order with periodic coefficients.

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