Find the infinite product .

The key is to recall the infinite product for sine:

.

Thus,

,

and letting *z*=*ıx*, then

.

To find the sine of an imaginary number, we use ; substituting *z*=*ıx*,

,

so

,

and thus

.

Letting *x*=1 then gives us our answer

.

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Tags: Hyperbolic Sine, Infinite Product, Math, Monday Math, Sine Product Formula

This entry was posted on November 30, 2009 at 12:32 am and is filed under Math/Science. You can follow any responses to this entry through the RSS 2.0 feed.
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