BUILT-IN MATHEMATICA SYMBOL

BesselI

gives the modified Bessel function of the first kind

.

MORE INFORMATION

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 .

FullSimplify and FunctionExpand include transformation rules for BesselI.

For certain special arguments, BesselI automatically evaluates to exact values.

BesselI can be evaluated to arbitrary numerical precision.

BesselI automatically threads over lists.

EXAMPLES

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Basic Examples (3)

Evaluate numerically:

Plot

:

Evaluate numerically:

In[1]:=

Out[1]=

Plot

:

In[1]:=

Out[1]=

In[1]:=

Out[1]=

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

and length

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: