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zetafunc.

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η(x), dirichlet's eta function?

how do i calculate dirichlet's eta function? like, η(2)? please show your working and how you got there, quoting and explaining formula used if necessary... thanks!

this isnt homework, sorry... but i want to ask it here, other forums dont answer, and yahoo answers drags...

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: η(x), dirichlet's eta function?

Hi zetafunc;

This is a simple formula:

For even integers the eta function is defined in terms of the bernoulli numbers.

They can be computed from the double sum developed by the Borweins. Whose work is extremely hard to follow.

All I remember is that this was created by using the Euler Transform which I only understand as a sequence accelerator.

All this and more is right here:

http://en.wikipedia.org/wiki/Dirichlet_eta_function

Go here for horrendously tough stuff:

http://mathworld.wolfram.com/DirichletEtaFunction.html

If you try to compute a few of these alternating series and run into trouble just post and I will help. Accelerating the convergence of sequences is my specialty.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.