History
Lambert published several examples of continued fractions in this form in 1768, and both Euler and Lagrange investigated similar constructions, but it was Carl Friedrich Gauss who utilized the clever algebraic trick described in the next section to deduce the general form of this continued fraction, in 1813.
Although Gauss gave the form of this continued fraction, he did not give a proof of its convergence properties. Bernhard Riemann and L.W. Thomé obtained partial results, but the final word on the region in which this continued fraction converges was not given until 1901, by Edward Burr Van Vleck.
Read more about this topic: Gauss's Continued Fraction
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