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IMSL_AIRY_AI

IMSL_AIRY_AI

The IMSL_AIRY_AI function evaluates the Airy function.

The airy function Ai(x) is defined to be:

The Bessel function Kv(x) is defined in IMSL_BESSK.

If x < -1.31Ïµ-2/3, then the answer will have no precision. If x < -1.31Ïµ-1/3, the answer will be less accurate than half precision. Here Ïµ is the machine precision.

x should be less than xmax so the answer does not underflow. Very approximately, xmax = {-1.5lns}2/3, where s = the smallest representable positive number.

If the keyword DERIVATIVE is set, then the airy function Aiâ²(x) is defined to be the derivative of the Airy function, Ai(x) (see the IMSL_AIRY_AI). If x < -1.31Ïµ-2/3, then the answer will have no precision. If x < -1.31Ïµ-1/3, the answer will be less accurate than half precision. Here Ïµ is the machine precision. x should be less than xmax so the answer does not underflow. Very approximately,

xmax = {-1.51lns}, where s is the smallest representable positive number.

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