So it is well-known that for [tex]n=2,3,...[/tex] the following equation holds(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\zeta(n)=\int_{x_{n}=0}^{1}\int_{x_{n-1}=0}^{1}\cdot\cdot\cdot\int_{x_{1}=0}^{1}\left(\frac{1}{1-\prod_{k=1}^{n}x_{k}}\right)dx_{1}\cdot\cdot\cdot dx_{n-1}dx_{n}[/tex]

My question is how can this relation be extended to [tex]n\in\mathbb{C}\setminus \{1\}[/tex], or some appreciable subset thereof (e.g. [tex]\Re(n)>1[/tex]) using fractional integration? Any help, suggestions, or even wanton derision, well, not that :yuck:, but anything useful would be counted kind.

Thanks,

-Ben

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Fractional Integration and the Riemann Zeta function

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**