Hi!

I've one more question this time about entire functions. How I can verify that the below function is entire function? And from where we have the last formula?

http://img46.imageshack.us/img46/5184/th2.th.png

Any help will be highly appreciated.

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- Jan 23rd 2010, 07:32 AMArczi1984Entire function
Hi!

I've one more question this time about entire functions. How I can verify that the below function is entire function? And from where we have the last formula?

http://img46.imageshack.us/img46/5184/th2.th.png

Any help will be highly appreciated. - Feb 9th 2010, 11:59 AMOpalg
The element is by definition the sum of the power series . Thus . This is a scalar-valued power series in with infinite radius of convergence, so it can be differentiated term by term and is analytic throughout . If in addition it never takes the value zero, then its logarithm can be defined as an entire function.