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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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Leon Aigret

Posts: 23
Registered: 12/1/09
Re: Derivation of limit of infinite quotient
Posted: Aug 22, 2012 9:44 AM
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On Wed, 22 Aug 2012 04:42:18 -0700 (PDT), Brad Cooper
<> wrote:

>f(n) = product(x^2-k^2*PI^2, k=1..n) and
>g(n) = product(x^2+k^2*PI^2, k=1..n)
>then limit n -> infinity of f(n)/g(n) = sin(x)/sinh(x)
>I am looking for a derivation and/or a proof of this.
>Could someone please give a pointer to where I can get started on this?

sin(x) = x product(1 - x^2 / (k PI)^2, k=1..inf) goes back to Euler.


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