Yad signature: positive self-power with a nonpositive branch

Read the equation

For x>0 the function returns xˣ+1. For x≤0 it explicitly returns one, avoiding non-real powers for many negative inputs. The positive branch tends to two as x approaches zero from above, so the chosen branch at zero makes the implemented function discontinuous there.

Terms & definitions

How it works

Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.

Assumptions & limits

Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.

Original context

	PrimaryAffinity: "Routing",
}

// =============================================================================
// 13.2 FAMILY FUNCTIONAL SIGNATURES
// =============================================================================

// FYad: F_Yad(x) = x^x + 1 (Foundation)
func FYad(x float64) float64 {
	if x <= 0 {
		return 1.0
	}
	return math.Pow(x, x) + 1.0
}

// FLashon: F_Lashon(x) = Σ_n a_n·sin(nπx) (Language - Fourier series)
func FLashon(x float64) float64 {
	sum := 0.0

FYad: F_Yad(x) = x^x + 1 (Foundation)

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