Dirichlet eta function

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English

Etymology

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

Proper noun

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Dirichlet eta function

Dirichlet eta function

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

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