The Ramanujan Journal

, Volume 15, Issue 2, pp 177-185

First online:

Expression for restricted partition function through Bernoulli polynomials

  • Boris Y. RubinsteinAffiliated withStowers Institute for Medical Research Email author 

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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.


Restricted partitions Bernoulli polynomials of higher order

Mathematics Subject Classification (2000)

11P81 11B68 11B37