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Euler's Continued Fraction

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Euler's continued fraction is the name given by Borwein et al. (2004, p. 30) to Euler's formula for the inverse tangent,

tan^(-1)x=x/(1+(x^2)/(3-x^2+(9x^2)/(5-3x^2+(25x^2)/(7-5x^2+...)))).

An even more famous continued fraction related to Euler which is perhaps a more appropriate recipient of the appellation "Euler's continued fraction" is the simple continued fraction for e, namely

e=[2;1,2,1,1,4,1,1,6,1,...].

See also

Continued Fraction, e Continued Fraction, Inverse Tangent

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References

Borwein, J.; Bailey, D.; and Girgensohn, R. "Euler's Continued Fraction." §1.8.2 in Experimentation in Mathematics: Computational Paths to Discovery. Wellesley, MA: A K Peters, p. 30, 2004.

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Euler's Continued Fraction

Cite this as:

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

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