The Theory of Partitions
Since the 18th century the theory of partitions has interested some of the best minds. While it seems to have little or no practical application, it has, in a certain sense, just the right degree of difficulty. The problems are far from trivial, but at the same time they are not so hard as to discourage any attempt at a solution. Besides, through the introduction by Euler (1707–1783) of generating functions, the highly developed apparatus of the theory of functions became available for the study of partitions. A further circumstance of great help in this study is the fact that the generating functions which occur in the theory of partitions and functions closely related to them belong to two important classes of functions, namely the theta functions and the modular functions, both of which have received much attention and have been most thoroughly investigated since the time of Jacobi (1804–1851).
KeywordsPartition Function Modular Form Theta Function Formal Power Series Power Series Expansion
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