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HankelH1

HankelH1[n, z]
gives the Hankel function of the first kind

MORE INFORMATION

Mathematical function, suitable for both symbolic and numerical manipulation.

is given by .

HankelH1[n, z] has a branch cut discontinuity in the complex z plane running from to .

For certain special arguments, HankelH1 automatically evaluates to exact values.

HankelH1 can be evaluated to arbitrary numerical precision.

HankelH1 automatically threads over lists.

EXAMPLES

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Basic Examples (3)

Evaluate numerically:

Plot the absolute value of

for various orders:

Series at the origin:

Series at infinity:

Evaluate numerically:

In[1]:=

Out[1]=

Plot the absolute value of

for various orders:

In[1]:=

Out[1]=

Series at the origin:

Series at infinity:

Scope (5)

Evaluate for complex arguments and orders:

Evaluate numerically to high precision:

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

HankelH1 threads element-wise over lists:

TraditionalForm formatting:

Generalizations & Extensions (2)

HankelH1 can be applied to a power series:

Find series expansions at infinity:

Properties & Relations (2)

Use FunctionExpand to convert to Bessel functions:

Integrate expressions with HankelH1:

Possible Issues (1)

HankelH1 does not automatically evaluate symbolically for half-integer arguments:

Use FunctionExpand to obtain an expanded form: