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An exact analytical solution of x coth x =αx2+ 1

Authors
Journal
Journal of Computational and Applied Mathematics
0377-0427
Publisher
Elsevier
Publication Date
Volume
2
Issue
1
Identifiers
DOI: 10.1016/0771-050x(76)90034-6

Abstract

Abstract The theory of complex variables is used to develop exact closed-form solutions of the transcendental equation x coth x = α x 2 + 1. The parameter α is considered to be real, and the reported analysis yields analytical expressions, in terms of elementary quadratures, for the real solutions x, as they depend on prescribed values of α.

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