Find

Hint: Define suitable sequence, use Abel's transformation to transform general term of series and Dirichle's theorem about uniform convergence of functional series. (Answer: )

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- Jan 21st 2010, 03:49 PMns1954Limit 5
Find

Hint: Define suitable sequence, use Abel's transformation to transform general term of series and Dirichle's theorem about uniform convergence of functional series. (Answer: ) - Jan 23rd 2010, 03:45 PMNonCommAlg
- Jan 23rd 2010, 06:15 PMns1954
I offer this direct proff. Function is defined for , by Dirichle criteria. Let

Now, for , and

Let . By Abel's transformation, we have

it's only neccessary to prove that series for is uniform convergent for

If

it's easy to prove that

and it's decreasing.

For we have

and for , so that

And anestly, I know very little about Riman's zeta-function.