:<math>\zeta(1) = 1 + \frac{1}{2} + \frac{1}{3} + \cdots = \infty</math>; dette er den [[harmonisk række|harmoniske række]].
:<math>\zeta(2) = 1 + \frac{1}{2^2} + \frac{1}{3^2} + \cdots = \frac{\pi^2}{6}</math>; demonstrationen af denne lighed er kendt som [[Baselproblemet]].
:<math>\zeta(3) = 1 + \frac{1}{2^3} + \frac{1}{3^3} + \cdots \approx 1.202\dots </math>; dette tal kaldes [[Apérys konstant]].
:<math>\zeta(4) = 1 + \frac{1}{2^4} + \frac{1}{3^4} + \cdots = \frac{\pi^4}{90}</math>
:<math>\zeta(5) = 1 + \frac{1}{2^5} + \frac{1}{3^5} + \cdots \approx 1.036\dots </math>
:<math>\zeta(6) = 1 + \frac{1}{2^6} + \frac{1}{3^6} + \cdots = \frac{\pi^6}{945}</math>
:<math>\zeta(7) = 1 + \frac{1}{2^7} + \frac{1}{3^7} + \cdots \approx 1.0083\dots</math>
:<math>\zeta(8) = 1 + \frac{1}{2^8} + \frac{1}{3^8} + \cdots = \frac{\pi^8}{9450}</math>
:<math>\zeta(9) = 1 + \frac{1}{2^9} + \frac{1}{3^9} + \cdots \approx 1.0020\dots</math>
:<math>\zeta(10) = 1 + \frac{1}{2^{10}} + \frac{1}{3^{10}} + \cdots = \frac{\pi^{10}}{93555}</math>
:<math>\zeta(12) = 1 + \frac{1}{2^{12}} + \frac{1}{3^{12}} + \cdots = \frac{691\pi^{12}}{638512875}</math>
:<math>\zeta(14) = 1 + \frac{1}{2^{14}} + \frac{1}{3^{14}} + \cdots = \frac{2\pi^{14}}{18243225}</math>
Videnskab Matematik Naturvidenskab