Euler product
From Encyclopedia of Mathematics
The infinite product
 |
where 
is a real number and 
runs through all prime numbers. This product converges absolutely for all 
. The analogous product for complex numbers 
converges absolutely for 
and defines in this domain the Riemann zeta-function
 |
Comments
See also Euler identity and Zeta-function.
How to Cite This Entry:
Euler product. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Euler_product&oldid=31829
Euler product. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Euler_product&oldid=31829
This article was adapted from an original article by S.A. Stepanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article