On a nonlinear relation for computing the overpartition function-Reference-Cited by-同舟云学术

On a nonlinear relation for computing the overpartition function

Published:2021-06-01 Issue:3 Volume:71 Page:535-542
ISSN:1337-2211
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Merca Mircea¹²

Affiliation:

1. Department of Mathematics, University of Craiova , 200585 , Craiova , Romania

2. Academy of Romanian Scientists , Ilfov 3, Sector 5 , Bucharest , Romania

Abstract

Abstract In 1939, H. S. Zuckerman provided a Hardy-Ramanujan-Rademacher-type convergent series that can be used to compute an isolated value of the overpartition function p (n). Computing p (n) by this method requires arithmetic with very high-precision approximate real numbers and it is complicated. In this paper, we provide a formula to compute the values of p (n) that requires only the values of p (k) with k ≤ n/2. This formula is combined with a known linear homogeneous recurrence relation for the overpartition function p (n) to obtain a simple and fast computation of the value of p (n). This new method uses only (large) integer arithmetic and it is simpler to program.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2021-0002/pdf

Reference31 articles.

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