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The Ramanujan Journal

, Volume 28, Issue 2, pp 253–271 | Cite as

A Hardy–Ramanujan–Rademacher-type formula for (r,s)-regular partitions

  • James Mc Laughlin
  • Scott Parsell
Article

Abstract

Let p r,s (n) denote the number of partitions of a positive integer n into parts containing no multiples of r or s, where r>1 and s>1 are square-free, relatively prime integers. We use classical methods to derive a Hardy–Ramanujan–Rademacher-type infinite series for p r,s (n).

Keywords

q-series Partitions Circle-method Hardy–Ramanujan–Rademacher 

Mathematics Subject Classification (2000)

11P82 05A17 11L05 11D85 11P55 11Y35 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Mathematics DepartmentWest Chester UniversityWest ChesterUSA

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