Notations J

$j_{\NVar{\nu},\NVar{m}}$: zeros of the Bessel function $J_{\nu}\left(x\right)$ ; §10.21(i)
${j^{\prime}_{\NVar{\nu},\NVar{m}}}$: zeros of the Bessel function derivative $J_{\nu}'\left(x\right)$ ; §10.21(i)
$J\left(\NVar{\tau}\right)$: Klein’s complete invariant; (23.15.7)
$J_{\NVar{k}}\left(\NVar{n}\right)$: Jordan’s function; (27.2.11)
$j_{\NVar{n}}(\NVar{z})=\mathsf{j}_{n}\left(z\right)$: notation used by Abramowitz and Stegun (1964); §10.1
(with $\mathsf{j}_{\NVar{n}}\left(\NVar{z}\right)$ : spherical Bessel function of the first kind)
$\mathsf{j}_{\NVar{n}}\left(\NVar{z}\right)$: spherical Bessel function of the first kind; (10.47.3)

$\mathcal{J}_{\NVar{\nu+\frac{1}{2}(m+1)}}(\NVar{\mathbf{T}})=A_{\nu}\left(% \mathbf{T}\right)/A_{\nu}\left(\boldsymbol{{0}}\right)$: notation used by Faraut and Korányi (1994, pp. 320–329); §35.1
(with $A_{\NVar{\nu}}\left(\NVar{\mathbf{T}}\right)$ : Bessel function of matrix argument (first kind))
$\widetilde{J}_{\NVar{\nu}}\left(\NVar{x}\right)$: Bessel function of imaginary order; (10.24.2)
$\mathbf{J}_{\NVar{\nu}}\left(\NVar{z}\right)$: Anger function; (11.10.1)
$J_{\NVar{\nu}}\left(\NVar{z}\right)$: Bessel function of the first kind; (10.2.2)
$\mathrm{jn}_{\NVar{n}}(\NVar{z},\NVar{q})=\operatorname{ge}_{n}\left(z,q\right)$: notation used by Campbell (1955); §28.1
(with $\operatorname{ge}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)$ : second solution, Mathieu’s equation)
$\mathrm{jnh}_{\NVar{n}}(\NVar{z},\NVar{q})=\operatorname{Ge}_{n}\left(z,q\right)$: notation used by Campbell (1955); §28.1
(with $\operatorname{Ge}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)$ : modified Mathieu function)