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Airy function of the second kind

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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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