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BesselI

BesselI
gives the modified Bessel function of the first kind .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • satisfies the differential equation .
  • BesselI has a branch cut discontinuity in the complex z plane running from to .
  • For certain special arguments, BesselI automatically evaluates to exact values.
  • BesselI can be evaluated to arbitrary numerical precision.
  • BesselI automatically threads over lists.
Evaluate numerically:
Plot :
Evaluate numerically:
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Plot :
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Click for copyable input
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Evaluate for complex arguments and parameters:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
BesselI threads element-wise over lists:
For half-integer indices, BesselI evaluates to elementary functions:
TraditionalForm formatting:
BesselI can be applied to a power series:
Inductance of a solenoid of radius and length with fixed numbers of turns per unit length:
Inductance per unit length of the infinite solenoid:
Use FullSimplify to simplify expressions with BesselI:
Integrate expressions involving BesselI:
Find limits of expressions involving BesselI:
With numeric arguments, half-integer Bessel functions are not automatically evaluated:
For symbolic arguments they are:
This can lead to major inaccuracies in machine-precision evaluation:
Continued fraction with arithmetic progression terms:
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