B How to write this in terms of ##\zeta (x)##?

  • B
  • Thread starter Thread starter MevsEinstein
  • Start date Start date
  • Tags Tags
    Terms
MevsEinstein
Messages
124
Reaction score
36
TL;DR Summary
I wrote $$\zeta (x+yi)$$ as ##\zeta(x)\zeta(yi) - \displaystyle\sum_{n=1}^\infty \frac{1}{n^x} *(\displaystyle\sum_{k \in S, \mathbb{Z}\S =n})##. I want to simplify the second term in terms of the zeta function so I can solve for ##\zeta (x)##.
How do I re-write $$\displaystyle\sum_{n=1}^\infty \frac{1}{n^x} *(\displaystyle\sum_{k \in S, \mathbb{Z}\S =n})$$ in terms of ##\zeta (x)## ? I want to solve for ##\zeta (x)## and simplifying the above expression in terms of ##\zeta (x)## would avoid repetition.
 
Last edited:
Physics news on Phys.org
You have to fix the latex in your post. You can use dollar signs instead of hashes to make the whole line display style which might make it look better.
 
Office_Shredder said:
You have to fix the latex in your post.
It took me forever to find the error. Turns out it was just a parentheses >D.
 
Oh wait instead of \ it gives me ##\S=##
 
MevsEinstein said:
How do I re-write $$\displaystyle\sum_{n=1}^\infty \frac{1}{n^x} *(\displaystyle\sum_{k \in S, \mathbb{Z}\S =n})$$
Before you can simplify the 2nd term, you need to say what is being summed.
 
Mark44 said:
Before you can simplify the 2nd term, you need to say what is being summed.
OOPS! $$\displaystyle\sum_{n=1}^\infty \frac{1}{n^x}*(\displaystyle\sum_{k \in S, \mathbb{Z} \S =n} \frac{1}{k^{yi}})$$ There you go. Note that ##\mathbb{Z} \S =n## is actually ##\mathbb{Z}##\S = n, I couldn't fix the bug.
 

Similar threads

Back
Top