# 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. S.A. Stepanov (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Euler_product&oldid=12289

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098