BUILT-IN MATHEMATICA SYMBOL

HankelH2

gives the Hankel function of the second kind

.

HankelH2 has a branch cut discontinuity in the complex z plane running from to .

For certain special arguments, HankelH2 automatically evaluates to exact values.

Evaluate numerically:

Plot the absolute value of

for various orders:

Series at the origin:

Series at infinity:

Evaluate numerically:

Out[1]=

Plot the absolute value of

for various orders:

Out[1]=

Series at the origin:

Out[1]=

Series at infinity:

Out[2]=

Evaluate for complex arguments and orders:

Evaluate numerically to high precision:

The precision of the output tracks the precision of the input:

HankelH2 threads element-wise over lists:

Use FunctionExpand to expand half-integer order HankelH2 into elementary functions:

HankelH2 can be applied to a power series:

Use FunctionExpand to convert to Bessel functions:

Integrate expressions with HankelH2:

HankelH2 does not automatically evaluate symbolically for half-integer arguments:

Use FunctionExpand to obtain expanded form: