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Theorems · Definition · functional analysis

FormalMultilinearSeries.coeff

{𝕜 : Type u} →
  {E : Type v} →
    [inst : NontriviallyNormedField 𝕜] →
      [inst_1 : NormedAddCommGroup E] → [inst_2 : NormedSpace 𝕜 E] → FormalMultilinearSeries 𝕜 𝕜 E → ℕ → E

The nth coefficient of p when seen as a power series.

Defined in
Mathlib.Analysis.Calculus.FormalMultilinearSeries
Cited by
30 results in Mathlib
Foundations
Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpace

Around this declaration

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

FormalMultilinearSeries.coeff_ofScalars · cited by 23FormalMultilinearSeries.c…FormalMultilinearSeries.apply_eq_prod_smul_coeff · cited by 19FormalMultilinearSeries.a…AnalyticAt.hasFPowerSeriesAt · cited by 7AnalyticAt.hasFPowerSerie…FormalMultilinearSeries.norm_apply_eq_norm_coef · cited by 3FormalMultilinearSeries.n…PeriodPair.hasFPowerSeriesOnBall_weierstrassPExcept · cited by 3PeriodPair.hasFPowerSerie…PeriodPair.coeff_weierstrassPExceptSeries · cited by 3PeriodPair.coeff_weierstr…FormalMultilinearSeries.coeff_fslope · cited by 2FormalMultilinearSeries.c…FormalMultilinearSeries.coeff_iterate_fslope · cited by 2FormalMultilinearSeries.c…HasFPowerSeriesAt.eq_pow_order_mul_iterate_dslope · cited by 2HasFPowerSeriesAt.eq_pow_…HasFPowerSeriesAt.iterate_dslope_fslope_ne_zero · cited by 2HasFPowerSeriesAt.iterate…Complex.regularizedHGFunSeries_coeff · cited by 2Complex.regularizedHGFunS…PeriodPair.weierstrassPExceptSeries_hasSum · cited by 2PeriodPair.weierstrassPEx…FormalMultilinearSeries.mkPiRing_coeff_eq · cited by 2FormalMultilinearSeries.m…PeriodPair.hasFPowerSeriesOnBall_derivWeierstrassPExcept · cited by 1PeriodPair.hasFPowerSerie…HasFPowerSeriesAt.has_fpower_series_dslope_fslope · cited by 1HasFPowerSeriesAt.has_fpo…DFunLike.coe · cited by 62936DFunLike.coeNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldFormalMultilinearSeries · cited by 615FormalMultilinearSeriesFormalMultilinearSeries.coeffCITED BYCITES

Cites5

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

Cited by30

Results whose statement or proof uses this declaration.