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Theorems · Theorem · complex analysis

Complex.hasSum_iff

∀ {α : Type u_1} {L : SummationFilter α} (f : α → ℂ) (c : ℂ),
  HasSum f c L ↔ HasSum (fun x => (f x).re) c.re L ∧ HasSum (fun x => (f x).im) c.im L
Defined in
Mathlib.Analysis.Complex.Basic
Cited by
2 results in Mathlib
Foundations
Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

hasSum_one_div_nat_pow_mul_cos · cited by 2hasSum_one_div_nat_pow_mu…hasSum_one_div_nat_pow_mul_sin · cited by 2hasSum_one_div_nat_pow_mu…Real · cited by 25697RealComplex · cited by 5565ComplexComplex.re · cited by 882Complex.reSummationFilter · cited by 607SummationFilterComplex.im · cited by 591Complex.imHasSum · cited by 518HasSumRCLike.hasSum_iff · cited by 1RCLike.hasSum_iffComplex.hasSum_iffCITED BYCITES

Cites7

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Cited by2

Results whose statement or proof uses this declaration.