Betufall Dirichlets

Betufall Dirichlets er fall skilgreint með Dirichlet-röð.

Skilgreining

$\beta (s)=\sum _{n=0}^{\mathrm{\infty }}\frac{(-1{)}^n}{(2n+1{)}^s},$

þar sem s er tvinntala.

Margfeldi

Fyrir tvinntölur s > 1:

$\beta (s)=\prod _{p\equiv 1\mathrm{m}\mathrm{o}\mathrm{d}4}\frac{1}{1-p^{-s}}\prod _{p\equiv 3\mathrm{m}\mathrm{o}\mathrm{d}4}\frac{1}{1+p^{-s}}.$

Tengt efni

• Etufall Dirichlets
• Lambdafall Dirichlets
• Zetufall Riemanns