It seems reasonable to think of continued fractions as generating a series of natural numbers. What's the convolution product on the series? Most generating functions are, well, functions. Is there a standard way of turning a continued fraction into a function? (Flajolet appears to have done a bunch of combinatorics work with continued fractions, but it's a little too dense for me to understand.) Rogers and Ramanujan showed how to q-deform continued fractions, replacing the 1/x step with q^n/x. From looking at continued fraction formulas for e and pi, however, it seems like for certain purposes we'd want linear or quadratic growth of the numerator instead of exponential. For the first case, an h-deformation that replaces the numerators with 1+nh instead of q^n seems promising. Has anyone seen work on that? -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com