DLMF:10.52.E1 (Q3747)

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DLMF:10.52.E1
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    Statements

    Defining formula
    𝗃 n ⁡ ( z ) , 𝗂 n ( 1 ) ⁡ ( z ) ∼ z n / ( 2 ⁢ n + 1 ) !! , asymptotically-equals spherical-Bessel-J 𝑛 𝑧 spherical-Bessel-I-1 𝑛 𝑧 superscript 𝑧 𝑛 double-factorial 2 𝑛 1 {\displaystyle{\displaystyle\mathsf{j}_{n}\left(z\right),{\mathsf{i}^{(1)}_{n}% }\left(z\right)\sim z^{n}/(2n+1)!!,}}
    0 references
    DLMF id
    DLMF:10.52.E1
    0 references
    Symbols used
    asymptotic equality
    Defining formula
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2adec
    0 references
    Q11277
    Defining formula
    !! double-factorial {\displaystyle{\displaystyle!!}}
    xml-id
    introduction.Sx4.p1.t1.r16.m7adec
    0 references
    modified spherical Bessel function
    Defining formula
    𝗂 n ( 1 ) ⁡ ( z ) spherical-Bessel-I-1 𝑛 𝑧 {\displaystyle{\displaystyle{\mathsf{i}^{(1)}_{\NVar{n}}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E7.m2adec
    0 references
    spherical Bessel function of the first kind
    Defining formula
    𝗃 n ⁡ ( z ) spherical-Bessel-J 𝑛 𝑧 {\displaystyle{\displaystyle\mathsf{j}_{\NVar{n}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E3.m2adec
    0 references
    Q11429
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1dec
    0 references
    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1dec
    0 references
     
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