Definition:Bessel Function/First Kind

Definition
A Bessel function of the first kind is a Bessel function which is nonsingular at the origin:


 * $\map {J_n} t = \dfrac {t^n} {2^n \, \map \Gamma {n + 1} } \paren {1 - \dfrac {t^2} {2 \paren {2 n + 2} } + \dfrac {t^4} {2 \times 4 \paren {2 n + 2} \paren {2 n + 4} } - \cdots}$