* Bill Gosper <billgosper@gmail.com> [Aug 24. 2015 16:52]:
Borwein*2, Exercise 3.7.10 (at least my old edition):
I do not think that there was another than the first edition. When I talked to Jon Borwein, suggesting a new edition would be a good thing, he essentially said "never gonna happen".
[...]
(Recall our old sum 1/fib(n) saga, where B&B seem to cop out and give only a Lambert series, but reading between the lines, there's a hairy closed form in terms of d/dq log qpochhammers.)
But there is a nice (theta convergence) "closed form", see section 2 of http://arxiv.org/abs/1202.6525 8^) The thing is more general than for 1/fib, it covers positive discriminants (of the recurrence). I have not attempted to crack negative discriminants, though that would appear worthwhile (I'd start looking at the Binet forms and try to carry the logic from positive discriminants over, looks doable). Best regards, jj
[...]