Airy function of the second kind
This functionality does not run in MATLAB.
airyBi(z
) airyBi(z
,n
)
airyBi(z)
represents the Airy function of
the second kind. The Airy functions airyAi(z)
and airyBi(z)
are
linearly independent solutions of the differential equation
.
The call airyBi(z)
is equivalent to airyBi(z,
0)
.
airyBi(z, n)
represents the nth
derivative of airyBi(z)
with respect to z.
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
.
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:
airyAi(x), airyAi(x, 1), airyBi(sin(x), 3)
For z = 0, special values are returned:
airyAi(0), airyBi(0, 1), airyAi(0, 27)
For n = 0, 1 and any symbolic , a symbolic call is returned:
airyAi(1), airyBi(x, 1)
floatingpoint values are returned for floatingpoint arguments:
airyBi(0.0), airyAi(3.24819, 1), airyBi(3.45 + 2.75*I);
The functions diff
, float
, limit
, and series
handle expressions
involving the Airy functions
diff(airyBi(x^2), x), float(airyAi(PI))
limit(airyAi(x), x = infinity), series(airyBi(x, 1), x = infinity, 4)
 

Arithmetical expression representing a nonnegative integer 
Arithmetical expression.
z