Abstract
The general analytic solutions of the following functional equations are exhibited: \[ \begin{gathered} {{\alpha (x + y)} / {[\alpha (x)\alpha (y)]}} = 1 + \varphi (x)\varphi (y)\psi (x + y), \hfill \\ {{\beta (x + y)} / {[\beta (x)\beta (y)]}} = \gamma (x) + \gamma (y) + \chi (x + y). \hfill \\ \end{gathered} \] These solutions are expressed in terms of Weierstrass elliptic functions; the special cases in which these reduce to elementary functions are also exhibited. Moreover, several remarkable formulae satisfied by Weierstrass elliptic functions are reported.
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