Theorems · Theorem · complex analysis

pi_mul_cot_pi_q_exp

∀ (z : UpperHalfPlane),
  ↑Real.pi * (↑Real.pi * ↑z).cot =
    ↑Real.pi * Complex.I - 2 * ↑Real.pi * Complex.I * ∑' (n : ℕ), Complex.exp (2 * ↑Real.pi * Complex.I * ↑z) ^ n

This is the version one probably wants, which is why the pi's are there.

Defined in: Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent
Cited by: 1 results in Mathlib
Foundations: Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound

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Complexstatement and proof · cited by 5,565
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Complex.ofRealstatement and proof · cited by 1,654
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tsumstatement and proof · cited by 1,148
Complex.Istatement and proof · cited by 866
neg_mulproof · cited by 654
UpperHalfPlanestatement and proof · cited by 626
one_divproof · cited by 624
Complex.expstatement and proof · cited by 612

Cited by1

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EisensteinSeries.qExpansion_identityproof · cited by 1