Talk:Zeta constant

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[edit] Question about ζ(2n)

If it is defined as:

\zeta(2n) = B_{2n} \frac{(-1)^{n+1} (2\pi)^{2n}}{2(2n)!}

Let's say that Pn is the nth term of the Taylor series for -\frac{1}{2} \cos 2\pi where the actual series is:

\cos x = \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n}}{(2n)!}

Then:

ζ(2n) = B2nPn

Is there any significance to that, or am I going around in a circle regarding the Taylor series for ex, sin x, and cos x, and the definition of ζ(n)? (unsigned post by User:JVz on 15 April)

Yes, to both questions: there's probably significance in that, and you are going around in circles. That's a part of what makes this area of math fun: its a hall of fun-house mirrors -- its all the same, but it isn't, but it is ... linas 05:34, 2 May 2006 (UTC)

[edit] Zeta derivatives

I just added the zeta derivatives at negative integers, but am not convinced these are right. By a calculation I'm doing, they seem to be off by a factor of n... Arghhhh. linas 05:34, 2 May 2006 (UTC)

Never mind, error appears to be elsewhere. linas 14:27, 2 May 2006 (UTC)

[edit] Definition

Does the definition of the Zeta constants include the values of derivatives of the Zeta function too, or just the values of the Zeta function ? Also, by Zeta constants, do we mean only those values obtained for integer values or for complex ones too ? MP (talk) 19:02, 8 May 2006 (UTC)

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