Dirichlet eta function

Named after German mathematician Peter Gustav Lejeune Dirichlet (1805–1859).

Dirichlet eta function

1. (mathematics, mathematical analysis) The alternating sum of the Dirichlet series expansion of the Riemann zeta function: ${\displaystyle \eta (s)=\sum _{n=1}^{\infty }{(-1)^{n-1} \over n^{s}}={\frac {1}{1^{s}}}-{\frac {1}{2^{s}}}+{\frac {1}{3^{s}}}-{\frac {1}{4^{s}}}+\cdots .}$