Notations Notations I Notations K

Notations J

$j_{\nu ,m}$

zeros of the Bessel function $J_{\nu }\left(x\right)$; §10.21(i)

$j_{\nu ,m}^{\prime }$

zeros of the Bessel function derivative $J_{\nu }^{\prime }\left(x\right)$; §10.21(i)

$J\left(\tau \right)$

Klein’s complete invariant; (23.15.7)

$J_k\left(n\right)$

Jordan’s function; (27.2.11)

$j_n(z)={𝗃}_n\left(z\right)$

notation used by Abramowitz and Stegun (1964); §10.1
(with ${𝗃}_n\left(z\right)$: spherical Bessel function of the first kind)

${𝗃}_n\left(z\right)$

spherical Bessel function of the first kind; (10.47.3)

${𝒥}_{\nu +\frac{1}{2}(m+1)}(𝐓)=A_{\nu }\left(𝐓\right)/A_{\nu }\left(𝟎\right)$

notation used by Faraut and Korányi (1994, pp. 320–329); §35.1
(with $A_{\nu }\left(𝐓\right)$: Bessel function of matrix argument (first kind))

${\tilde{J}}_{\nu }\left(x\right)$

Bessel function of imaginary order; (10.24.2)

${𝐉}_{\nu }\left(z\right)$

Anger function; (11.10.1)

$J_{\nu }\left(z\right)$

Bessel function of the first kind; (10.2.2)

${\mathrm{jn}}_n(z,q)={\mathrm{ge}}_n(z,q)$

notation used by Campbell (1955); §28.1
(with ${\mathrm{ge}}_n(z,q)$: second solution, Mathieu’s equation)

${\mathrm{jnh}}_n(z,q)={\mathrm{Ge}}_n(z,q)$

notation used by Campbell (1955); §28.1
(with ${\mathrm{Ge}}_n(z,q)$: modified Mathieu function)

Notations I Notations K

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