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Theorems · Theorem · complex analysis

FormalMultilinearSeries.coeff_ofScalars

∀ {𝕜 : Type u_3} [inst : NontriviallyNormedField 𝕜] {p : ℕ → 𝕜} {n : ℕ},
  (FormalMultilinearSeries.ofScalars 𝕜 p).coeff n = p n
Defined in
Mathlib.Analysis.Analytic.OfScalars
Cited by
23 results in Mathlib
Foundations
Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedField

Around this declaration

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

AnalyticAt.hasFPowerSeriesAt · cited by 7AnalyticAt.hasFPowerSerie…Complex.one_div_sub_pow_hasFPowerSeriesOnBall_zero · cited by 3Complex.one_div_sub_pow_h…PeriodPair.coeff_weierstrassPExceptSeries · cited by 3PeriodPair.coeff_weierstr…PeriodPair.summable_weierstrassPExceptSummand · cited by 3PeriodPair.summable_weier…PeriodPair.hasFPowerSeriesOnBall_weierstrassPExcept · cited by 3PeriodPair.hasFPowerSerie…AnalyticAt.analyticAt_localInverse · cited by 2AnalyticAt.analyticAt_loc…Real.one_div_sub_pow_hasFPowerSeriesOnBall_zero · cited by 2Real.one_div_sub_pow_hasF…hasFPowerSeriesAt_clog_one · cited by 2hasFPowerSeriesAt_clog_oneComplex.regularizedHGFunSeries_coeff · cited by 2Complex.regularizedHGFunS…Complex.one_div_one_sub_cpow_hasFPowerSeriesOnBall_zero · cited by 2Complex.one_div_one_sub_c…Complex.one_div_sub_sq_sub_one_div_sq_hasFPowerSeriesOnBall_zero · cited by 1Complex.one_div_sub_sq_su…PeriodPair.weierstrassPExcept_eq_tsum · cited by 1PeriodPair.weierstrassPEx…PeriodPair.hasFPowerSeriesOnBall_derivWeierstrassPExcept · cited by 1PeriodPair.hasFPowerSerie…UpperHalfPlane.qExpansionFormalMultilinearSeries_apply_norm · cited by 1UpperHalfPlane.qExpansion…UpperHalfPlane.qExpansionFormalMultilinearSeries_coeff · cited by 1UpperHalfPlane.qExpansion…NontriviallyNormedField · cited by 8742NontriviallyNormedFieldmul_one · cited by 3885mul_oneFinset.univ · cited by 3473Finset.univFinset.prod_congr · cited by 646Finset.prod_congrsmul_apply · cited by 229smul_applyFinset.prod_const_one · cited by 100Finset.prod_const_oneFormalMultilinearSeries.ofScalars · cited by 68FormalMultilinearSeries.o…FormalMultilinearSeries.coeff · cited by 30FormalMultilinearSeries.c…ContinuousMultilinearMap.mkPiAlgebraFin · cited by 29ContinuousMultilinearMap.…List.prod_ofFn · cited by 3List.prod_ofFnFormalMultilinearSeries.coeff…CITED BYCITES

Cites10

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

Cited by23

Results whose statement or proof uses this declaration.