About the Project
Notations

Notations J

j ν , m
zeros of the Bessel function Jν(x); §10.21(i)
j ν , m
zeros of the Bessel function derivative Jν(x); §10.21(i)
J ( τ )
Klein’s complete invariant; (23.15.7)
J k ( n )
Jordan’s function; (27.2.11)
j n ( z ) = 𝗃 n ( z )
notation used by Abramowitz and Stegun (1964); §10.1
(with 𝗃n(z): spherical Bessel function of the first kind)
𝗃 n ( z )
spherical Bessel function of the first kind; (10.47.3)
𝒥 ν + 1 2 ( m + 1 ) ( 𝐓 ) = A ν ( 𝐓 ) / A ν ( 𝟎 )
notation used by Faraut and Korányi (1994, pp. 320–329); §35.1
(with Aν(𝐓): Bessel function of matrix argument (first kind))
J ~ ν ( x )
Bessel function of imaginary order; (10.24.2)
𝐉 ν ( z )
Anger function; (11.10.1)
J ν ( z )
Bessel function of the first kind; (10.2.2)
jn n ( z , q ) = ge n ( z , q )
notation used by Campbell (1955); §28.1
(with gen(z,q): second solution, Mathieu’s equation)
jnh n ( z , q ) = Ge n ( z , q )
notation used by Campbell (1955); §28.1
(with Gen(z,q): modified Mathieu function)