coeff_mul_C — Mathlib

English

The coefficient at index 0 of φ is equal to the constant coefficient: coeff(0)(φ) = constantCoeff φ.

Русский

Коэффициент при индексе 0 формы φ равен её константному коэффициенту: coeff(0)(φ) = constantCoeff φ.

LaTeX

$$$\operatorname{coeff}(0) (\phi) = \operatorname{constantCoeff}(\phi)$$$

Lean4

@[simp]
theorem coeff_mul_C (n : σ →₀ ℕ) (φ : MvPowerSeries σ R) (a : R) : coeff n (φ * C a) = coeff n φ * a := by
  simpa using coeff_add_mul_monomial n 0 φ a

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