Definition:Bessel Function/First Kind

Definition
A Bessel function of the first kind of order $n$ is a Bessel function which is non-singular at the origin

It is usually denoted $\map {J_n} x$, where $x$ is the dependent variable of the instance of Bessel's equation to which $\map {J_n} x$ forms a solution.

Also known as
Some sources (for whatever reason) do not address Bessel functions of the second kind, and as a consequence refer to Bessel functions of the first kind simply as Bessel functions.

Some sources use $p$ to denote the order of the Bessel function.

Also see

 * Series Expansion of Bessel Function of the First Kind‎
 * Bessel Function of the First Kind of Negative Integer Order‎


 * Definition:Bessel Function of the Second Kind


 * Definition:Modified Bessel Function of the First Kind
 * Definition:Modified Bessel Function of the Second Kind