coeffN.apple

-- aₙ, bₙ, cₙ, dₙ in Kuhl+Giardina
λxs.λys.λn.
  { sum ← [(+)/x]
  ; tieSelf ← [({.x)⊳x]; Δ ← [(-)\~(tieSelf x)]
  ; dxs ⟜ Δ xs; dys ⟜ Δ ys
  ; dts ⟜ [√(x^2+y^2)]`dxs dys
  ; dxss ⟜ ((%)`dxs dts); dyss ⟜ ((%)`dys dts)
  ; pts ⟜ (+)Λₒ 0 dts ; T ⟜}. pts
  ; n ⟜ ℝn; k ⟜ 2*n*𝜋
  ; scaleRad ← [k*x%T]
  ; cosDiffs ⟜ (-)\~([cos.(scaleRad x)]' pts)
  ; sinDiffs ⟜ (-)\~([sin.(scaleRad x)]' pts)
  ; c ⟜ T%(2*n^2*𝜋^2)
  ; aₙ ← c*sum ((*)`dxss cosDiffs)
  ; bₙ ← c*sum ((*)`dxss sinDiffs)
  ; cₙ ← c*sum ((*)`dyss cosDiffs)
  ; dₙ ← c*sum ((*)`dyss sinDiffs)
  ; (aₙ,bₙ,cₙ,dₙ)
  }