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Rademacher-Type Formulas For Restricted Partition And Overpartition Functions, Andrew Sills
Rademacher-Type Formulas For Restricted Partition And Overpartition Functions, Andrew Sills
Department of Mathematical Sciences Faculty Publications
A collection of Hardy-Ramanujan-Rademacher type formulas for restricted partition and overpartition functions is presented, framed by several biographical anecdotes.
Towards An Automation Of The Circle Method, Andrew Sills
Towards An Automation Of The Circle Method, Andrew Sills
Department of Mathematical Sciences Faculty Publications
The derivation of the Hardy-Ramanujan-Rademacher formula for the number of partitions of n is reviewed. Next, the steps for finding analogous formulas for certain restricted classes of partitions or overpartitions is examined, bearing in mind how these calculations can be automated in a CAS. Finally, a number of new formulas of this type which were conjectured with the aid of Mathematica are presented along with results of a test for their numerical accuracy.