The Kronecker limit formula is an important result in the theory of modular forms and number theory. It relates the behavior of certain L-functions to the special values of those functions at integers. Specifically, it provides a way to compute the special value of an L-function associated with a point on a certain modular curve. The formula can be stated in the context of the Dedekind eta function and the Eisenstein series.
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This normalization of the first Kronecker limit formula follows from the Fourier expansion of the completed nonholomorphic Eisenstein series. At , , so the nonconstant terms sum to . The constant terms supply . Combining them gives the Dedekind eta function expression, with the Euler--Mascheroni constant.