# Natural Logarithm Approximated by Continued Fractions

Natural Logarithm Approximated by Continued Fractions

Continued fractions provide a very effective toolset for approximating functions. Usually the continued fraction expansion of a function approximates the function better than its Taylor or Fourier series. This Demonstration compares the quality of three approximations to . One is the Taylor series and the other two are continued fraction expansions. The first continued fraction expansion can be obtained as a canonical even contraction of a continued fraction using Euler's method to transform a series to an -fraction. The other continued fraction expansion was developed by the author as a canonical even contraction from the first one.

ln(1+x)

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