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On a Functional Differential Equation of Determinantal Type

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H. W. Braden, J.G.B. Byatt-Smith

Classical Analysis and ODEs · Submitted 17 Apr 1998

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim These equations essentially characterise the Weierstrass $\wp$-function and its degenerations. %\quad\quad x+y+z=0. $$

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arXiv IDmath/9804082 (version 1)
Pith IDMRV3KFYF, Pith's permanent record of this paper and its review
CitationH. W. Braden, J.G.B. Byatt-Smith. "On a Functional Differential Equation of Determinantal Type." arXiv:math/9804082 (1998). https://pith.science/paper/MRV3KFYF
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The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We solve the functional equations $$ \begin{vmatrix} 1 & 1 & 1 f(x) & f(y) & f(z) f\sp{\prime}(x)& f\sp{\prime}(y)& f\sp{\prime}(z) \end{vmatrix} =0,\quad\quad \begin{vmatrix} 1 & 1 & 1 f(x) & g(y) & h(z) \\ f\sp{\prime}(x)& g\sp{\prime}(y)& h\sp{\prime}(z) \end{vmatrix} =0, for suitable functions $f$, $g$ and $h$ subject to $x+y+z=0$. These equations essentially characterise the Weierstrass $\wp$-function and its degenerations. %\quad\quad x+y+z=0. $$

background contribution method result interpretation main claim

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We solve the functional equations $$ \begin{vmatrix} 1 & 1 & 1 f(x) & f(y) & f(z) f\sp{\prime}(x)& f\sp{\prime}(y)& f\sp{\prime}(z) \end{vmatrix} =0,\quad\quad \begin{vmatrix} 1 & 1 & 1 f(x) & g(y) & h(z) \\ f\sp{\prime}(x)& g\sp{\prime}(y)& h\sp{\prime}(z) \end{vmatrix} =0, for suitable functions $f$, $g$ and $h$ subject to $x+y+z=0$. contribution 0.87 0.91 0.26 asserted 0.99
s1 These equations essentially characterise the Weierstrass $\wp$-function and its degenerations. %\quad\quad x+y+z=0. $$ interpretation 0.85 0.61 0.79 asserted 0.95

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We solve the functional equations $$ \begin{vmatrix} 1 & 1 & 1 f(x) & f(y) & f(z) f\sp{\prime}(x)& f\sp{\prime}(y)& f\sp{\prime}(z) \end{vmatrix} =0,\quad\quad \begin{vmatrix} 1 & 1 & 1 f(x) & g(y) & h(z) \\ f\sp{\prime}(x)& g\sp{\prime}(y)& h\sp{\prime}(z) \end{vmatrix} =0, for suitable functions $f$, $g$ and $h$ subject to $x+y+z=0$. These equations essentially characterise the Weierstrass $\wp$-function and its degenerations. %\quad\quad x+y+z=0. $$

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