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Theorems · Definition · complex analysis

Function.Periodic.cuspFunction

ℝ → (ℂ → ℂ) → ℂ → ℂ

The function q ↦ f (invQParam h q), extended by a non-canonical choice of limit at 0.

Defined in
Mathlib.Analysis.Complex.Periodic
Cited by
18 results in Mathlib
Foundations
Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

UpperHalfPlane.cuspFunction · cited by 46UpperHalfPlane.cuspFuncti…Function.Periodic.cuspFunction_eq_of_nonzero · cited by 4Periodic.cuspFunction_eq_…UpperHalfPlane.eq_cuspFunction · cited by 4UpperHalfPlane.eq_cuspFun…Function.Periodic.eq_cuspFunction · cited by 4Periodic.eq_cuspFunctionFunction.Periodic.cuspFunction_zero_of_zero_at_inf · cited by 3Periodic.cuspFunction_zer…Function.Periodic.differentiableAt_cuspFunction_zero · cited by 3Periodic.differentiableAt…Function.Periodic.cuspFunction_add · cited by 2Periodic.cuspFunction_addFunction.Periodic.cuspFunction_neg · cited by 2Periodic.cuspFunction_negFunction.Periodic.cuspFunction_smul · cited by 2Periodic.cuspFunction_smulFunction.Periodic.differentiableAt_cuspFunction · cited by 2Periodic.differentiableAt…UpperHalfPlane.exp_decay_sub_atImInfty · cited by 2UpperHalfPlane.exp_decay_…Function.Periodic.exp_decay_sub_of_bounded_at_inf · cited by 2Periodic.exp_decay_sub_of…Function.Periodic.tendsto_nhds_zero · cited by 2Periodic.tendsto_nhds_zeroUpperHalfPlane.cuspFunction_mul_zero · cited by 2UpperHalfPlane.cuspFuncti…Function.Periodic.boundedAtFilter_cuspFunction · cited by 1Periodic.boundedAtFilter_…Real · cited by 25697RealComplex · cited by 5565ComplexCompl.compl · cited by 2925Compl.complnhdsWithin · cited by 1912nhdsWithinFunction.update · cited by 502Function.updateFilter.limUnder · cited by 47Filter.limUnderFunction.Periodic.invQParam · cited by 18Periodic.invQParamPeriodic.cuspFunctionCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by19

Results whose statement or proof uses this declaration.