Dirichlet eta function

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

Dirichlet eta function

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