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+ wz-1(f2 + 1/6) + 2ri(a 1/2)(3 1/2), where X(t) = -log(1-e-2,rt) (the principal value), 0 _ _a 1, 0 0. This formula was first proved in [2], and its applications to the theory of partitions have also been investigated (see [2; 3]). The method we employ in this paper is essentially that of Rademacher [4]. Although our method is still based on the Mellin transform technique and the theory of the Hurwitz zeta-functions, we have made a thorough revision of Rademacher's original method, and thus a very short and direct proof of the functional equation can be given. It may be noted that if we define a function A(z, a, ,B) by

A proof of a functional equation related to the theory of partitions.