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Theorems · Theorem · number theory

tendsto_sub_mul_tsum_nat_cpow

Filter.Tendsto (fun s => (s - 1) * ∑' (n : ℕ), 1 / ↑n ^ s) (nhdsWithin 1 {s | 1 < s.re}) (nhds 1)

The residue of ζ(s) at s = 1 is equal to 1, expressed using tsum.

Defined in
Mathlib.NumberTheory.LSeries.RiemannZeta
Cited by
1 results in Mathlib
Foundations
Depth 305 from the axioms · uses propext, Classical.choice, Quot.sound

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