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KelvinBer

KelvinBer[z]
gives the Kelvin function .
KelvinBer
gives the Kelvin function .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • For positive real values of parameters, . For other values, is defined by analytic continuation.
  • KelvinBer has a branch cut discontinuity in the complex z plane running from to .
  • For certain special arguments, KelvinBer automatically evaluates to exact values.
  • KelvinBer can be evaluated to arbitrary numerical precision.
Evaluate numerically:
Plot :
Series at the origin:
Evaluate numerically:
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Click for copyable input
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Plot :
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Click for copyable input
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Series at the origin:
In[1]:=
Click for copyable input
Out[1]=
Evaluate for complex arguments and orders:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
KelvinBer threads element-wise over lists:
TraditionalForm formatting:
KelvinBer can be applied to a power series:
Solve the Kelvin differential equation:
Plot the resistance of a wire with circular cross section versus AC frequency (skin effect):
Use FullSimplify to simplify expressions involving Kelvin functions:
Use FunctionExpand to expand Kelvin functions of half-integer orders:
Integrate expressions involving Kelvin functions:
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