Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Using a technique due to Gauss a lot of special functions can be expressed as continued fractions.

What applications of this are there within mathematics and number theory?

share|cite|improve this question
One application mentioned in that page is: Analytic continuation of $_2 F_1$ type. – user58512 Jan 27 '13 at 21:17

Computationally, CF expansions of hypergeometric functions can be very useful. In particular, one might want to remember that the series for hypergeometric functions can, for certain parameter values, be only convergent for arguments within the unit disk. In contrast, the CF expansions usually have a larger domain of convergence, usually a half-plane or a slit plane.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.