On a Functional Differential Equation of Determinantal Type
Classical Analysis and ODEs
2007-05-23 v1 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
solv-int
Abstract
We solve the functional equations \begin{vmatrix} 1 & 1 & 1 f(x) & f(y) & f(z) f\sp{\prime}(x)& f\sp{\prime}(y)& f\sp{\prime}(z) \end{vmatrix} =0,\quad\quad \begin{vmatrix} 1 & 1 & 1 f(x) & g(y) & h(z) \\ f\sp{\prime}(x)& g\sp{\prime}(y)& h\sp{\prime}(z) \end{vmatrix} =0, for suitable functions $f$, $g$ and $h$ subject to $x+y+z=0$. These equations essentially characterise the Weierstrass $\wp$-function and its degenerations. %\quad\quad x+y+z=0.
Cite
@article{arxiv.math/9804082,
title = {On a Functional Differential Equation of Determinantal Type},
author = {H. W. Braden and J. G. B. Byatt-Smith},
journal= {arXiv preprint arXiv:math/9804082},
year = {2007}
}
Comments
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