Can someone me check something.

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A user questioned the necessity of restricting the variable "x" to integers in the equations of the Riemann Zeta Function on a Wolfram MathWorld page. They noted that while the integral is valid for all real values of "x," the discussion surrounding the infinite sum seemed unnecessarily limited to integers. Other participants confirmed that the summation's dummy variable does not impact the argument's value, indicating that the restriction to integers is indeed unwarranted. The conversation highlighted a misunderstanding regarding the notation and context of the equations. Ultimately, the consensus is that the page's suggestion to limit "x" to integers is incorrect.
uart
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Hi, I was reading a derivation over at mathworld.wolfram and I struck something that looks simple enough but I can't quite see it. I think it might be a mistake in the web-page but I'd just like to get second (or 3rd 4th etc) opinion on it.

The page in question is here : http://mathworld.wolfram.com/RiemannZetaFunction.html"

I know there's some heavy stuff on that page but trust me that my issue is a fairly simple one. If you scroll down past the preamble and graphs until you come to the numbered equations, the part I have an issue with is in equations 1 through to 7.

Specifically the part where it says "If x is an integer n, then we have the identity" (just after numbered equation 1). In that section from equation 1 through 7 I just can't see anything at all that would require x be restricted to integers. Is it just me or do you think that the page is in error when it suggests that x needs to be an integer here?

Thanks in advance.
 
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The integral is valid for all values of "x", the discussion of the infinite sum is specialized for "x" integer, and an integer is commonly denoted by "n".

So i don't see your problem.
 
dextercioby said:
The integral is valid for all values of "x", the discussion of the infinite sum is specialized for "x" integer, and an integer is commonly denoted by "n".

So i don't see your problem.

Yes I know that the integral is valid for real x (actually x>1), but I don't see why the sum is restricted to integer values of the argument.

Please read it carefully and note that the summation dummy variable (k in that text) has absolutely nothing to do with whether or not the argument of the function (x or n in that text) is integer or otherwise.
 
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On a better reading, you're right, it makes no sense to restrict the discussion to natural values of "x", as it doesn't affect the calculation.
 
That's what I thought. Thanks for verifying it Kurt.
 
His name is Daniel, by the way, not Kurt
 
arildno said:
His name is Daniel, by the way, not Kurt

Doh I see it now, Kurt Lewin is the author of one of the quotes in his sig. Blush :blushing:
 
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