* rwg@sdf.lonestar.org <rwg@sdf.lonestar.org> [Jul 12. 2008 16:01]:
[...]
but still nothing about plain old
inf ==== n \ q > ------, / n ==== q - 1 n = 1
with which we could sum the reciprocal Fibonacci numbers.
Have you checked Borwein/Borwein "Pi and the AGM"? pp.91-101 might make you happy.
Sadly not)-: They denote this Lambert series -L(q), but never give it in terms of Thetas or ThetaPrimes. Despite the section heading, they never deliver Sum 1/Fib(n) except in terms of L. It may well be inexpressible without some new special function. (They do give Sum 1/Fib(2*n+1) in Thetas, which is easy.) --rwg They say the brain is your largest sex organ. I don't believe it. I've gotten > 5000 pen!s enhancement spams (sic), and not one for enhancing my brain.