On a Functional Differential Equation of Determinantal Type
Braden, H. W. ; Byatt-Smith, J. G. B.
arXiv, 9804082 / Harvested from arXiv
Text on arXiv
We solve the functional equations $$ \begin{vmatrix} 1 & 1 & 1 f(x) & f(y) & f(z) f\sp{\prime}(x)& f\sp{\prime}(y)& f\sp{\prime}(z) \end{vmatrix} =0,\quad\quad \begin{vmatrix} 1 & 1 & 1 f(x) & g(y) & h(z) \\ f\sp{\prime}(x)& g\sp{\prime}(y)& h\sp{\prime}(z) \end{vmatrix} =0, for suitable functions $f$, $g$ and $h$ subject to $x+y+z=0$. These equations essentially characterise the Weierstrass $\wp$-function and its degenerations. %\quad\quad x+y+z=0. $$
Publié le : 1998-04-17
Classification:  Mathematics - Classical Analysis and ODEs,  Mathematical Physics,  Nonlinear Sciences - Exactly Solvable and Integrable Systems,  39B22, 30D05, 33E05 
@article{9804082,
     author = {Braden, H. W. and Byatt-Smith, J. G. B.},
     title = {On a Functional Differential Equation of Determinantal Type},
     journal = {arXiv},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9804082}
}

Braden, H. W.; Byatt-Smith, J. G. B. On a Functional Differential Equation of Determinantal Type. arXiv, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/9804082/