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BesselK

BesselK
gives the modified Bessel function of the second kind .
MORE INFORMATION
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • satisfies the differential equation .
  • BesselK has a branch cut discontinuity in the complex z plane running from to .
  • For certain special arguments, BesselK automatically evaluates to exact values.
  • BesselK can be evaluated to arbitrary numerical precision.
  • BesselK automatically threads over lists.
EXAMPLESCLOSE ALL
Basic Examples   (3)
Evaluate numerically:
Plot :
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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Click for copyable input
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Scope   (6)
Evaluate for complex arguments and parameters:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
BesselK threads element-wise over lists:
For half-integer index, BesselK evaluates to elementary functions:
TraditionalForm formatting:
Generalizations & Extensions   (1)
BesselK can be applied to a power series:
Applications   (1)
Specific heat of the relativistic ideal gas per particle:
Find the ultra-relativistic limit:
Properties & Relations   (2)
Use FullSimplify to simplify Bessel functions:
Integrate expressions involving BesselK:
Possible Issues   (1)
With numeric arguments, half-integer Bessel functions are not automatically evaluated:
For symbolic arguments they are:
This can lead to inaccuracies in machine-precision evaluation:
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