Abstract
We solve the functional equation $$\frac{{G(y + x)}}{{G(y - x)}} = \frac{{f(y) + f(x)}}{{f(y) - f(x)}}$$ where (f, G) are a pair of meromorphic functions. This equation comes from a convolution identity related to Brownian motion, and its solutions are given by certain Jacobi elliptic functions.
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