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BesselI

BesselI[n, z]
gives the modified Bessel function of the first kind I_n(z).
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • I_n(z) satisfies the differential equation z^2y^('')+zy^'-(z^2+n^2)y=0.
  • BesselI[n, z] has a branch cut discontinuity in the complex z plane running from -infty to 0.
  • For certain special arguments, BesselI automatically evaluates to exact values.
  • BesselI can be evaluated to arbitrary numerical precision.
  • BesselI automatically threads over lists.
EXAMPLESCLOSE ALL
Scope   (5)
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:
Generalizations & Extensions   (1)
BesselI can be applied to a power series:
Applications   (1)
Inductance of a solenoid of radius r and length a with fixed numbers of turns per unit length:
Inductance per unit length of the infinite solenoid:
Properties & Relations   (4)
Use FullSimplify to simplify expressions with BesselI:
Integrate expressions involving BesselI:
Find limits of expressions involving BesselI:
Possible Issues   (1)
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:
Neat Examples   (1)
Continued fraction with arithmetic progression terms:
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