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Function Repository Resource:

 StruveKelvinStei

Source Notebook

Evaluate the Struve–Kelvin stei function

Contributed by: Jan Mangaldan

ResourceFunction["StruveKelvinStei"][z]

gives the Struve–Kelvin function stei(z).

ResourceFunction["StruveKelvinStei"][n,z]

gives the Struve–Kelvin function stein(z).

Details

Mathematical function, suitable for both symbolic and numerical manipulation.
For positive real values of parameters, stein(z)= Im(Hn(z​e3π​i/4)), where H is the StruveH function. For other values, stei is defined by analytic continuation.
ResourceFunction["StruveKelvinStei"][n,z] has a branch cut discontinuity in the complex z plane running from -∞ to 0.
ResourceFunction["StruveKelvinStei"][z] is equivalent to ResourceFunction["StruveKelvinStei"][0,z].
For certain special arguments, ResourceFunction["StruveKelvinStei"] automatically evaluates to exact values.
ResourceFunction["StruveKelvinStei"] can be evaluated to arbitrary numerical precision.
ResourceFunction["StruveKelvinStei"] automatically threads over lists.

Examples

Basic Examples (2) 

Evaluate numerically:

In[1]:=
ResourceFunction["StruveKelvinStei"][2.5]
Out[1]=

Plot stei(x):

In[2]:=
Plot[ResourceFunction["StruveKelvinStei"][x], {x, 0, 10}]
Out[2]=

Scope (4) 

Evaluate for complex arguments and orders:

In[3]:=
ResourceFunction["StruveKelvinStei"][1 - I, -2.5 + I]
Out[3]=

Evaluate to high precision:

In[4]:=
N[ResourceFunction["StruveKelvinStei"][1, 10], 50]
Out[4]=

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

In[5]:=
ResourceFunction[ "StruveKelvinStei"][1, 10.000000000000000000000000000000000000]
Out[5]=

StruveKelvinStei threads elementwise over lists:

In[6]:=
ResourceFunction["StruveKelvinStei"][{1, 2, 3}, 1.0]
Out[6]=

Properties and Relations (1) 

Use FunctionExpand to expand Struve–Kelvin functions of half-integer orders:

In[7]:=
FunctionExpand[ResourceFunction["StruveKelvinStei"][1/2, x]]
Out[7]=

Version History

  • 1.0.0 – 04 March 2021

Source Metadata

  • Citation:
    • McLachlan, N. W., Meyers, A. L., "The ster and stei functions." The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Series 7, vol. 21, 425-436, 1936. DOI: 10.1080/14786443608561595

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