DLMF:10.60.E5 (Q3780)

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DLMF:10.60.E5
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    Statements

    Defining formula
    𝗒 n ⁡ ( 2 ⁢ z ) = n ! ⁢ z n + 1 ⁢ ∑ k = 0 n n - k + 1 2 k ! ⁢ ( 2 ⁢ n - k + 1 ) ! ⁢ ( 𝗃 n - k 2 ⁡ ( z ) - 𝗒 n - k 2 ⁡ ( z ) ) , spherical-Bessel-Y 𝑛 2 𝑧 𝑛 superscript 𝑧 𝑛 1 superscript subscript 𝑘 0 𝑛 𝑛 𝑘 1 2 𝑘 2 𝑛 𝑘 1 spherical-Bessel-J 𝑛 𝑘 2 𝑧 spherical-Bessel-Y 𝑛 𝑘 2 𝑧 {\displaystyle{\displaystyle\mathsf{y}_{n}\left(2z\right)=n!z^{n+1}\sum_{k=0}^% {n}\frac{n-k+\frac{1}{2}}{k!(2n-k+1)!}{\left({\mathsf{j}_{n-k}^{2}}\left(z% \right)-{\mathsf{y}_{n-k}^{2}}\left(z\right)\right)},}}
    0 references
    DLMF id
    DLMF:10.60.E5
    0 references
    Symbols used
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
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    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.m2abdec
    0 references
    Q11429
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1ddec
    0 references
    Q11428
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1adec
    0 references
    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1adec
    0 references
     
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