Riemann zeta function

Meaning

Noun

• The function ζ defined by the Dirichlet series $\backslash textstyle\; \backslash zeta(s)=\backslash sum\_\{n=1\}^\backslash infty\; \backslash frac\; 1\; \{n^s\}\; =\; \backslash frac1\{1^s\}\; +\; \backslash frac1\{2^s\}\; +\; \backslash frac1\{3^s\}\; +\; \backslash frac1\{4^s\}\; +\; \backslash cdots$, which is summable for points s in the complex half-plane with real part > 1; the analytic continuation of said function, being a holomorphic function defined on the complex numbers with pole at 1.
• A usage of (a specified value of) the Riemann zeta function, such as in an equation.

Related

Similar words

• Euler–Riemann zeta function

Broader meaning words

• analytic function, zeta function