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Topic: Derivation of limit of infinite quotient
Replies: 3   Last Post: Aug 22, 2012 4:15 PM

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Karl-Olav Nyberg

Posts: 277
Registered: 12/6/04
Re: Derivation of limit of infinite quotient
Posted: Aug 22, 2012 4:15 PM
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On Wednesday, August 22, 2012 1:42:18 PM UTC+2, Brad Cooper wrote:
> If
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> f(n) = product(x^2-k^2*PI^2, k=1..n) and
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> g(n) = product(x^2+k^2*PI^2, k=1..n)
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> then limit n -> infinity of f(n)/g(n) = sin(x)/sinh(x)
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> I am looking for a derivation and/or a proof of this.
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> Could someone please give a pointer to where I can get started on this?
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> Regards :-)


You might get some inspiration from this:

http://www.jstor.org/discover/10.2307/3029628?uid=3738744&uid=2129&uid=2&uid=70&uid=4&sid=21100996956843

KON



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