Airy function of the second kind

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.


airyBi(z, n)


airyBi(z) represents the Airy function of the second kind. The Airy functions of the first and second kind are linearly independent solutions of the differential equation .

airyBi(z, n) represents the n-th derivative of airyBi(z) with respect to z.

airyBi(z) is equivalent to airyBi(z, 0).

For n ≥ 2, derivatives of the Airy functions are automatically expressed in terms of the Airy functions and their first derivative. See Example 1.

airyBi returns special values for z = 0 and z = ±∞. For all other symbolic values of z, unevaluated function calls are returned. See Example 2.

Environment Interactions

When called with floating-point arguments, this functions is sensitive to the environment variable DIGITS which determines the numerical working precision.


Example 1

Second and higher derivatives of Airy functions are rewritten in terms of Airy functions and their first derivatives:

airyBi(x), airyBi(x, 1), airyBi(sin(x), 3)

Example 2

For z = 0, special values are returned:

airyBi(0), airyBi(0, 1), airyBi(0, 27)

For n = 0, n = 1 and any symbolic z ≠ 0, z ≠ ±∞, a symbolic call is returned:

airyBi(-1), airyBi(x, 1)

Floating-point values are returned for floating-point arguments:

airyBi(0.0), airyBi(-3.24819, 1), airyBi(-3.45 + 2.75*I)

Example 3

diff, float, limit, series, and other functions handle expressions involving the Airy functions:

diff(airyBi(x^2), x)


limit(airyBi(-x), x = infinity)

series(airyBi(x, 1), x = infinity)



Arithmetical expression


Arithmetical expression representing a nonnegative integer

Return Values

Arithmetical expression.

Overloaded By


See Also

MuPAD Functions

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