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Laguerre's Repeated Fraction

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The continued fraction

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

See also

Continued Fraction, Lambert's Method

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References

Hardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea, pp. 13 and 21, 1959.Watson, G. N. "Ramanujan's Note Books." J. London Math. Soc. 6, 137-153, 1931.Watson, G. N. "The Mock Theta Functions (II)." Proc. London Math. Soc. 42, 274-304, 1937.

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Laguerre's Repeated Fraction

Cite this as:

Weisstein, Eric W. "Laguerre's Repeated Fraction." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LaguerresRepeatedFraction.html

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