is convergent?

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- May 7th 2009, 03:55 AM #1

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- May 7th 2009, 04:08 AM #2

- May 8th 2009, 02:24 PM #3

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- May 8th 2009, 11:44 PM #4

- May 9th 2009, 07:19 AM #5
Remembering the identity...

(1)

... the condition for which the sum...

(2)

... converges becomes...

(3)

If is a pure real variable, then , i.e. the function you see here...

It is remarkable the fact that is real for and complex [with real and imaginary part...] for . In this case the condition (3) is satisfied for and and here the (2) is...

(4)

But what does it happen when has an imaginary part that is not 0?... that's the problem ...

Kind regards