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==Application to continued fractions== By applying a limiting argument to [[Gauss's continued fraction]] it can be shown that ...

...rthogonal polynomials developed in the late 19th century from a study of [[continued fraction]]s by [[Pafnuty Chebyshev|P. L. Chebyshev]] and was pursued by [[A ...

(After cancellation the numerator/denominator fractions are entries {{oeis|A092676}}/{{oeis|A092677}} in the [[OEIS]]; without canc ===Continued fraction expansion=== ...

...with |''z''| ≥ 1 it can be [[analytic continuation|analytically continued]] along any path in the complex plane that avoids the branch points 1 and i ...tric equation describes how fundamental solutions change when analytically continued around paths in the ''z'' plane that return to the same point. ...

For the actual computation of numerical values, [[Gauss's continued fraction]] provides a useful expansion: This continued fraction converges for all complex ''z'', provided only that ''s'' is not a ...

...roduced the Legendre polynomials. In the late 19th century, the study of [[continued fraction]]s to solve the [[moment problem]] by [[Pafnuty Chebyshev|P. L. Ch ...