DLMF: Notations J

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$\mathop{j_{{\nu,m}}\/}\nolimits$: zeros of the Bessel function $\mathop{J_{{\nu}}\/}\nolimits\!\left(x\right)$ ; §10.21(i)
$\mathop{{j^{{\prime}}_{{\nu,m}}}\/}\nolimits$: zeros of the Bessel function derivative ${\mathop{J_{{\nu}}\/}\nolimits^{{\prime}}}\!\left(x\right)$ ; §10.21(i)
$\mathop{J\/}\nolimits\!\left(\tau\right)$: Klein’s complete invariant; (23.15.7)
$\mathop{\mathbf{J}_{{\nu}}\/}\nolimits\!\left(z\right)$: Anger function; (11.10.1)
$\mathop{J_{{\nu}}\/}\nolimits\!\left(z\right)$: Bessel function of the first kind; (10.2.2)
$\mathop{\widetilde{J}_{{\nu}}\/}\nolimits\!\left(x\right)$: Bessel function of imaginary order; (10.24.2)

$\mathcal{J}_{{\nu+\frac{1}{2}(m+1)}}(\mathbf{T})=\mathop{A_{{\nu}}\/}\nolimits\!\left(\mathbf{T}\right)/\mathop{A_{{\nu}}\/}\nolimits\!\left(\boldsymbol{{0}}\right)$: notation used by Faraut and Korányi (1994, pp. 320–329); §35.1
(with $\mathop{A_{{\nu}}\/}\nolimits\!\left(\mathbf{T}\right)$ : Bessel function of matrix argument (first kind))
$\mathop{J_{{k}}\/}\nolimits\!\left(n\right)$: Jordan’s function; (27.2.11)
$j_{n}(z)=\mathop{\mathsf{j}_{{n}}\/}\nolimits\!\left(z\right)$: notation used by Abramowitz and Stegun (1964); §10.1
(with $\mathop{\mathsf{j}_{{n}}\/}\nolimits\!\left(z\right)$ : spherical Bessel function of the first kind)
$\mathop{\mathsf{j}_{{n}}\/}\nolimits\!\left(z\right)$: spherical Bessel function of the first kind; (10.47.3)
$\mathrm{jn}_{n}(z,q)=\mathop{\mathrm{ge}_{{n}}\/}\nolimits\!\left(z,q\right)$: notation used by Campbell (1955); ¶ ‣ §28.1
(with $\mathop{\mathrm{ge}_{{n}}\/}\nolimits\!\left(z,q\right)$ : second solution, Mathieu’s equation)
$\mathrm{jnh}_{n}(z,q)=\mathop{\mathrm{Ge}_{{n}}\/}\nolimits\!\left(z,q\right)$: notation used by Campbell (1955); ¶ ‣ §28.1
(with $\mathop{\mathrm{Ge}_{{n}}\/}\nolimits\!\left(z,q\right)$ : modified Mathieu function)