A question at math.SE is asking for references. The fraction is quite nice! Check it out and post some references if you know of any.

I found this at arxiv, but it doesn't apply to Zeta.

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A question at math.SE is asking for references. The fraction is quite nice! Check it out and post some references if you know of any.

I found this at arxiv, but it doesn't apply to Zeta.

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I found that H. J. Brothers is submiting an article with the tittle "*The Euler zeta function, continued fractions, and pi*" see here.

riemann zeta continued fraction: a paper`by S.Apodaca`

, another one`by CVIJOVIC AND KLINOWSKI`

, a`MO post`

, a`Wolfram demo tool`

. Above inks perhaps not related to MSE question but there are more google results. $\endgroup$ – Mirko Apr 11 '14 at 17:22