Argh! From: 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. Jörg>Have you checked Borwein/Borwein "Pi and the AGM"? pp.91-101 might make you happy. rwg>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 But did they give it in terms of q-digamma and I somehow missed or rejected it? http://mathworld.wolfram.com/ReciprocalFibonacciConstant.html claims they do! Could it have been added in a later edition? My (autographed) first edition is unhandy. Here I thought I had capped my 40 yr search, and the answer is sitting in Mathworld. The only consolation is that my answer doesn't use 𝜗s, so we get this peculiarity: EllipticTheta[2, 0, ϕ^-2]^2 = 2 Im[QPolyGamma[0, 1/2 + I π/(4 Log[ϕ]), ϕ^-2]]/Log[ϕ] ~ 3.26379 Can this generalize, or is it only about the Golden Ratio? --rwg