Special values of L-functions

In mathematics, the study of special values of L-functions is a subfield of number theory devoted to generalising formulae such as the Leibniz formula for π, namely 1 − 1 3 + 1 5 − 1 7 + 1 9 − ⋯ = π 4 , {\displaystyle 1\,-\,{\frac {1}{3}}\,+\,{\frac {1}{5}}\,-\,{\frac {1}{7}}\,+\,{\frac {1}{9}}\,-\,\cdots \;=\;{\frac {\pi }{4}},\! } by the recognition that expression on the left-hand side is also L ( 1 ) {\displaystyle L(1)} where L ( s ) {\displaystyle L(s)} is the Dirichlet L-function for the field of Gaussian rational numbers. This formula is a special case of the analytic class number formula, and in those terms reads that the Gaussian field has class number 1.

Source: Wikipedia — Special values of L-functions (CC BY-SA 4.0)