--- Gerald McGarvey <Gerald.McGarvey@comcast.net> wrote:
Regarding the following equality shown in http://mathworld.wolfram.com/ContinuedFractionConstant.html
[A + D, A + 2D, A + 3D,...] =
I_A/D(2/D) ---------- I_1+A/D(2/D)
for real A and D not = 0
Has this been proven for complex D not = 0? Based on a few calculations, it seems likely to be true. ...
The continued fraction [A, A, A, ...] converges for all complex A except the open interval of the imaginary axis {iy | -2 < y < 2}. On that basis, I would expect the continued fraction formula to hold, and be a meromorphic function of A and D, when D is nonzero or A is outside the divergence interval. Gene ______________________________________________________ Yahoo! for Good Donate to the Hurricane Katrina relief effort. http://store.yahoo.com/redcross-donate3/