Definition:Modified Bessel Function/First Kind
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Definition
A modified Bessel function of the first kind of order $n$ is a modified Bessel function which is non-singular at the origin.
It is usually denoted $\map {I_n} x$, where $x$ is the dependent variable of the instance of Bessel's modified equation to which $\map {I_n} x$ forms a solution.
Also known as
Some sources (for whatever reason) do not address modified Bessel functions of the second kind, and as a consequence refer to modified Bessel functions of the first kind simply as modified Bessel functions.
Some sources use $p$ to denote the order of the modified Bessel function.
Also see
Source of Name
This entry was named for Friedrich Wilhelm Bessel.
Sources
- 1965: Murray R. Spiegel: Theory and Problems of Laplace Transforms ... (previous) ... (next): Chapter $1$: The Laplace Transform: Some Special Functions: $\text {II}$. Bessel functions: $5$