DLMF:10.49.E18 (Q3720)

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DLMF:10.49.E18
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    Statements

    Defining formula
    𝗃 n 2 ⁡ ( z ) + 𝗒 n 2 ⁡ ( z ) = ∑ k = 0 n s k ⁢ ( n + 1 2 ) z 2 ⁢ k + 2 . spherical-Bessel-J 𝑛 2 𝑧 spherical-Bessel-Y 𝑛 2 𝑧 superscript subscript 𝑘 0 𝑛 subscript 𝑠 𝑘 𝑛 1 2 superscript 𝑧 2 𝑘 2 {\displaystyle{\displaystyle{\mathsf{j}_{n}^{2}}\left(z\right)+{\mathsf{y}_{n}% ^{2}}\left(z\right)=\sum_{k=0}^{n}\frac{s_{k}(n+\frac{1}{2})}{z^{2k+2}}.}}
    0 references
    DLMF id
    DLMF:10.49.E18
    0 references
    Symbols used
    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.m2acdec
    0 references
    spherical Bessel function of the second kind
    Defining formula
    𝗒 n ⁡ ( z ) spherical-Bessel-Y 𝑛 𝑧 {\displaystyle{\displaystyle\mathsf{y}_{\NVar{n}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E4.m2acdec
    0 references
    Q11429
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1ldec
    0 references
    Q11428
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1idec
    0 references
    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1odec
    0 references
    DLMF:10.49.E17
    Defining formula
    s k ⁢ ( n ) subscript 𝑠 𝑘 𝑛 {\displaystyle{\displaystyle s_{k}(n)}}
    xml-id
    C10.S49.XMD1.m1adec
    0 references
     
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