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AdvancedMathAiry Method

Computes both Airy functions and their derivatives.

Namespace:  Meta.Numerics.Functions
Assembly:  Meta.Numerics (in Meta.Numerics.dll) Version: 4.1.4
public static SolutionPair Airy(
	double x


Type: SystemDouble
The argument.

Return Value

Type: SolutionPair
The values of Ai(x), Ai'(x), Bi(x), and Bi'(x).

Airy functions are solutions to the Airy differential equation:

The Airy functions appear in quantum mechanics in the semi-classical WKB solution to the wave functions in a potential.

For negative arguments, Ai(x) and Bi(x) are oscillatory. For positive arguments, Ai(x) decreases exponentially and Bi(x) increases exponentially with increasing x.

This method simultaneously computes both Airy functions and their derivatives. If you need both Ai and Bi, it is faster to call this method once than to call AiryAi(Double) and AiryBi(Double) separately. If on, the other hand, you need only Ai or only Bi, and no derivative values, it is faster to call the appropriate method to compute the one you need.

See Also