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On two elementary functional identities
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DOI：10.1007/s40840-025-01964-9.png)
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Abstract
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In this paper, we establish two elementary functional identities closely related to a pair of functions satisfying f(x,a)g(b,c)+f(x,b)g(c,a)+f(x,c)g(a,b)=0.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} f(x,a)g(b,c)+f(x,b)g(c,a)+f(x,c)g(a,b)=0. \end{aligned}$$\end{document}The latter may serve as a prototype for the classical Weierstrass theta identity. Some special cases of these two functional identities are also presented.
Keywords:
The Weierstrass theta identity
Induction hypothesis
(f
g)-inversion
q-series
Theta function
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B
IF:
1.2
Papers:
143
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0
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