Computer Algebra and Rademacher-Type Partition Formulas

One of the most impressive and useful contributions to twentieth century number theory was the circle method of Ramanujan, Hardy, and Littlewood, with subsequent improvements by Rademacher. The application of the circle method to the problem of finding a convergent series representation for p ( n ), the number of partitions of n involves a number of nontrivial calculations and delicate estimates, some of which are amenable to automation in a computer algebra system such as Mathematica . I will share Rademacher-type formulas for various restricted partition functions which were obtained with the aid of the computer.