Airy function of the second kind
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airyBi(z
) 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.
When called with floatingpoint 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)
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)
Floatingpoint values are returned for floatingpoint arguments:
airyBi(0.0), airyBi(3.24819, 1), airyBi(3.45 + 2.75*I)
diff
, float
, limit
, series
, and other functions
handle expressions involving the Airy functions:
diff(airyBi(x^2), x)
float(airyBi(PI))
limit(airyBi(x), x = infinity)
series(airyBi(x, 1), x = infinity)
 

Arithmetical expression representing a nonnegative integer 
Arithmetical expression.
z