Airy function of the second kind
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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
airyBi(z) with respect to
airyBi(z) is equivalent to
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
= 0 and
z = ±∞. For all other
symbolic values of z,
unevaluated function calls are returned. See Example 2.
When called with floating-point arguments, this functions is
sensitive to the environment variable
DIGITS which determines
the numerical working precision.
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)
z = 0, special values are returned:
airyBi(0), airyBi(0, 1), airyBi(0, 27)
n = 0,
n = 1 and any
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)
limit(airyBi(-x), x = infinity)
series(airyBi(x, 1), x = infinity)
Arithmetical expression representing a nonnegative integer