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Lambert's Continued Fraction

As Gauss showed in 1812, the hyperbolic tangent can be written using a continued fraction as

tanhx=x/(1+(x^2)/(3+(x^2)/(5+...)))

(Wall 1948, p. 349; Olds 1963, p. 138).

See also

Continued Fraction, Hyperbolic Tangent

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References

Olds, C. D. Continued Fractions. New York: Random House, 1963.Wall, H. S. Analytic Theory of Continued Fractions. New York: Chelsea, 1948.

Referenced on Wolfram|Alpha

Lambert's Continued Fraction

Cite this as:

Weisstein, Eric W. "Lambert's Continued Fraction." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LambertsContinuedFraction.html

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