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Bauer-Muir Transformation

A transformation formula for continued fractions (Lorentzen and Waadeland 1992) which can, for example, be used to prove identities such as

1/(1+(2+q)/(1+(2+q^2)/(1+(2+q^3)/(1+...))))=1/(2+q/(2+q+(q^2)/(2+q^2+(q^3)/(2+q^3+...))))

(Berndt et al. 2000).

See also

Continued Fraction, Rogers-Ramanujan Continued Fraction

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References

Berndt, B. C.; Huang, S.-S.; Sohn, J.; and Son, S. H. "Some Theorems on the Rogers-Ramanujan Continued Fraction in Ramanujan's Lost Notebook." Trans. Amer. Math. Soc. 352, 2157-2177, 2000.Lorentzen, L. and Waadeland, H. Continued Fractions with Applications. Amsterdam, Netherlands: North-Holland, p. 76, 1992.

Referenced on Wolfram|Alpha

Bauer-Muir Transformation

Cite this as:

Weisstein, Eric W. "Bauer-Muir Transformation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Bauer-MuirTransformation.html

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