# 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: $5$