Error terms from the continued fractions of e^{1/s} and √(v/u) tanh(1/√(uv)) assemble into weighted sums that recover the original functions.
Hurwitz, ¨Uber die Entwicklung complexer Gr¨ oßen in Kettenbr¨ uche,Acta Math.11(1887–1888), 187–200
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Error terms for continued fractions of $e^{1/s}$ and $\sqrt{\frac{v}{u}}\tanh\!\Bigl(\frac{1}{\sqrt{uv}}\Bigr)$
Error terms from the continued fractions of e^{1/s} and √(v/u) tanh(1/√(uv)) assemble into weighted sums that recover the original functions.