Talk:Reciprocal Fibonacci constant: Difference between revisions
→No closed-form formula?: +expand |
Bill Gosper (talk | contribs) →There IS a closed form!: new section |
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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. [[Special:Contributions/76.111.56.192|76.111.56.192]] ([[User talk:76.111.56.192|talk]]) 22:16, 20 February 2010 (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. [[Special:Contributions/76.111.56.192|76.111.56.192]] ([[User talk:76.111.56.192|talk]]) 22:16, 20 February 2010 (UTC) |
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:The expression on MathWorld involves [[Jacobi's elliptic functions]], which usually aren't allowed to count as [[closed-form expression]]s. It does show that our article could use expansion, though. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 22:23, 20 February 2010 (UTC) |
:The expression on MathWorld involves [[Jacobi's elliptic functions]], which usually aren't allowed to count as [[closed-form expression]]s. It does show that our article could use expansion, though. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 22:23, 20 February 2010 (UTC) |
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== There IS a closed form! == |
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The already referenced http://mathworld.wolfram.com/ReciprocalFibonacciConstant.html gives a cumbersome but closed expression in terms of the first derivative of the rather well-known [[https://en.wikipedia.org/wiki/Q-gamma_function|q-Gamma function]], which I have simplified to [http://gosper.org/recipfib.pdf gosper.org/recipfib.pdf] (Horrors! Original research?). [[https://en.wikipedia.org/wiki/Fibonacci_number]] repeats the erroneous no closed form claim.--[[User:Bill Gosper|Bill Gosper]] ([[User talk:Bill Gosper|talk]]) 07:41, 29 August 2014 (UTC) |
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Revision as of 07:41, 29 August 2014
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 a cumbersome but closed expression in terms of the first derivative of the rather well-known [function], which I have simplified to gosper.org/recipfib.pdf (Horrors! Original research?). [[1]] repeats the erroneous no closed form claim.--Bill Gosper (talk) 07:41, 29 August 2014 (UTC)