Airy Function Ai(x) and Bi(x) Calculator

Enter x to compute the Airy functions Ai(x) and Bi(x). Evaluated with series and asymptotic expansions, with a curve chart.

Input

Enter a value of x to compute the Airy functions Ai(x) and Bi(x).

Value of x

Enter any real number (e.g. 0, 1, -2.5).

Ai(x) at x = 0

0.3550280539

Bi(x) at x = 0

0.6149266274

Input x

Graph of Ai(x) and Bi(x)

Ai(x)

Bi(x)

The Airy functions are the two independent solutions of the differential equation y''(x) = x y(x), written Ai(x) and Bi(x).
Ai(x) decays exponentially for large positive x, while Bi(x) grows rapidly. For large negative x both functions oscillate.
This tool uses a Maclaurin series for small x and an asymptotic expansion for large positive x.
At x=0, Ai(0)=0.3550280539 and Bi(0)=0.6149266274.
The chart range is clamped for readability because Bi(x) diverges quickly on the positive side.

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