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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)
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 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 Γq 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)
This article is rated Stub-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
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)
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 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 Γq 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)