# Approximating the Riemann Zeta Function with Continued Fractions

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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 shows the high quality of a continued fraction expansion to approximate the Riemann ζ function.

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Contributed by: Andreas Lauschke (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

This is a special case of a continued fraction expansion for the polylog function, as is .

With the definitions

and

,

the continued fraction approximation for the polylog function can be written as

.

In particular, for ,

as well as

.

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