GOLDEN BASIS FUNCTIONS · Psi returns ψ_k(x)

Read the equation

This relation defines Psi returns ψ_k(x) in the source section “GOLDEN BASIS FUNCTIONS · Psi returns ψ_k(x)”. Evaluates oscillatory sine or cosine terms using the stated phase or frequency. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to them.

Terms & definitions

The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.

How it works

1. Read Psi returns ψ_k(x) as the quantity being defined or updated by this relation.

2. Evaluates oscillatory sine or cosine terms using the stated phase or frequency.

3. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

Assumptions & limits

• This source expression was recovered from the pinned code revision. Its presence does not establish that the associated program was built, run, or scientifically validated.

Original context

// =============================================================================
// GOLDEN BASIS FUNCTIONS
// =============================================================================

// GoldenBasis provides golden ratio basis functions
type GoldenBasis struct{}

// Psi returns ψ_k(x) = sin(2πφ^k · x) + cos(2πφ^k · x)
func (GoldenBasis) Psi(k int, x float64) float64 {
	arg := 2.0 * math.Pi * math.Pow(PHI, float64(k)) * x
	return math.Sin(arg) + math.Cos(arg)
}

// BasisVector generates basis vector for N terms
func (gb GoldenBasis) BasisVector(x float64, N int) []float64 {
	result := make([]float64, N)
	for k := 0; k < N; k++ {
		result[k] = gb.Psi(k, x)

Psi returns ψ_k(x) = sin(2πφ^k · x) + cos(2πφ^k · x)

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