A Rademacher-Type Formula for

A Rademacher-Type Formula for pod(n)

A Rademacher Type Formula for Partitions and Overpartitions

A Rademacher-type convergent series formula which generalizes the Hardy-Ramanujan-Rademacher formula for the number of partitions of n and the Zuckerman formula for the Fourier coefficients of θ4(0 | τ)−1 is presented. 1. Background 1.1. Partitions. A partition of an integer n is a representation of n as a sum of positive integers, where the order of the summands (called parts) is considered ir...

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

Let pr,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 pr,s(n).

a cauchy-schwarz type inequality for fuzzy integrals

نامساوی کوشی-شوارتز در حالت کلاسیک در فضای اندازه فازی برقرار نمی باشد اما با اعمال شرط هایی در مسئله مانند یکنوا بودن توابع و قرار گرفتن در بازه صفر ویک می توان دو نوع نامساوی کوشی-شوارتز را در فضای اندازه فازی اثبات نمود.

Efficient implementation of the Hardy{--}Ramanujan{--}Rademacher formula

We describe how the Hardy–Ramanujan–Rademacher formula can be implemented to allow the partition function p(n) to be computed with softly optimal complexity O(n) and very little overhead. A new implementation based on these techniques achieves speedups in excess of a factor 500 over previously published software and has been used by the author to calculate p(10), an exponent twice as large as i...