A new approach to the representation of trigonometric and hyperbolic functions by infinite products

An innovative technique is developed for obtaining infinite product representations for some elementary functions. The technique is based on the comparison of alternative expressions of Green's functions constructed by two different methods. Some standard boundary value problems are considered...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2008-08, Vol.344 (1), p.521-534
Main Author: Melnikov, Yu.A.
Format: Article
Language:English
Subjects:
Elementary functions
Exact sciences and technology
Green's functions
Infinite products
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Partial differential equations
Partial differential equations, boundary value problems
Sciences and techniques of general use
Special functions
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Summary:An innovative technique is developed for obtaining infinite product representations for some elementary functions. The technique is based on the comparison of alternative expressions of Green's functions constructed by two different methods. Some standard boundary value problems are considered posed for two-dimensional Laplace equation on regions of a regular configuration. Classical closed analytic form of Green's functions for such problems are compared against those obtained by the method of images in the form of infinite products. This yields a number of new infinite product representations for trigonometric and hyperbolic functions.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2008.03.010