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Perron's Continued Fraction

Perron's continued fraction is defined by

int_0^z(t^mu)/(1+t)dt=z/(mu+1+((mu+1)^2z)/((mu+2)-(mu+1)z+((mu+2)^2z)/((mu+3)-(mu+2)z+...)))

for mu>-1 and -1<z<=1 (Perron 1954-1957, p. 18; Borwein et al. 2004, p. 35).

See also

Continued Fraction

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References

Borwein, J.; Bailey, D.; and Girgensohn, R. "Perron's Continued Fraction." §1.8.4 Experimentation in Mathematics: Computational Paths to Discovery. Wellesley, MA: A K Peters, 2004.Perron, O. Die Lehre von den Kettenbrüchen, Vol. 2. Stuttgart, Germany: Teubner, 1954-1957.

Referenced on Wolfram|Alpha

Perron's Continued Fraction

Cite this as:

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

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