prove that converges for and defines a function which has an essential singularity at P=0.

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- Apr 24th 2010, 08:24 PMKat-Messential singularity
prove that converges for and defines a function which has an essential singularity at P=0.

- Apr 24th 2010, 09:26 PMchisigma
The series...

(1)

... is a Laurent series with an infinite numers of negative powers of z, so that in is has an essential singularity. If we consider (1) as a 'geometric series' we have...

(2)

... and the (1) converges for , not symply for ...

Kind regards

- Apr 25th 2010, 11:20 AMKat-M
the exponent of 2 is not -2j. it is . so it wont be geometric.

- Apr 25th 2010, 11:38 PMchisigma
Very sorry for my misreading! (Headbang)...

According to the 'Stirling approximation' is...

(1)

... so that is...

(2)

Now the series absolutely converges and therefore the same is for the series ...

Kind regards