Talk:Reciprocal Fibonacci constant

Nonperiodicity of continued fraction represetantion

Gandalf61 had removed recently added assertion about nonperiodicity of continued fraction representation of ψ. The truth is, yes, the assertion was really unsourced and interesting question remains - is ψ a quadratic irrational? Similar is with Apéry's constant ζ(3) - there are also no sources about this, or perhaps I've missed something. Series of both constants have infinitely many terms. --xJaM (talk) 14:06, 15 January 2008 (UTC)

No closed-form formula?

The claim in this article that there is no closed-form representation of the reciprocal sum seems to be contradicted by Wolfram's website. One should be more specific when making this claim; does it mean that the series has no closed form representation? Does it mean that the number itself is non-algebraic? If it's the former then it's wrong, since Wolfram's website solves the series and cites papers over 20 years old which had the original solution in them. 76.111.56.192 (talk) 22:16, 20 February 2010 (UTC)

The expression on MathWorld involves Jacobi's elliptic functions, which usually aren't allowed to count as closed-form expressions. It does show that our article could use expansion, though. —David Eppstein (talk) 22:23, 20 February 2010 (UTC)

There IS a closed form!

The already referenced http://mathworld.wolfram.com/ReciprocalFibonacciConstant.html gives several closed expressions in terms of θ₂ and the first derivative of the rather well-known [function]. I have written and tested the simplest Mathworld formula in gosper.org/recipfib.pdf. [[1]] repeats the erroneous no closed form claim. I think disqualifying θ₂ and Γ_q as non-closed forms is almost as retrogressive as disqualifying complex numbers as non-numeric. Is there really a Wikipedia standard for closed form?--Bill Gosper (talk) 07:41, 29 August 2014 (UTC)