DLMF:2.8.E27 (Q962)

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DLMF:2.8.E27
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    Statements

    Defining formula
    B s ⁢ ( ξ ) = - A s ′ ⁢ ( ξ ) + 1 ξ 1 / 2 ⁢ ∫ 0 ξ ( ψ ⁢ ( v ) ⁢ A s ⁢ ( v ) - ( ν + 1 2 ) ⁢ A s ′ ⁢ ( v ) ) ⁢ d v v 1 / 2 , subscript 𝐵 𝑠 𝜉 superscript subscript 𝐴 𝑠 ′ 𝜉 1 superscript 𝜉 1 2 superscript subscript 0 𝜉 𝜓 𝑣 subscript 𝐴 𝑠 𝑣 𝜈 1 2 superscript subscript 𝐴 𝑠 ′ 𝑣 𝑣 superscript 𝑣 1 2 {\displaystyle{\displaystyle B_{s}(\xi)=-A_{s}^{\prime}(\xi)+\frac{1}{\xi^{1/2% }}\int_{0}^{\xi}\left(\psi(v)A_{s}(v)-\left(\nu+\tfrac{1}{2}\right)A_{s}^{% \prime}(v)\right)\frac{\mathrm{d}v}{v^{1/2}},}}
    0 references
    DLMF id
    DLMF:2.8.E27
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1afdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3afdec
    0 references
    Q11086
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C2.S8.XMD21.m1cdec
    0 references
    Q11088
    Defining formula
    A s ⁢ ( ξ ) subscript 𝐴 𝑠 𝜉 {\displaystyle{\displaystyle A_{s}(\xi)}}
    xml-id
    C2.S8.XMD23.m1bdec
    0 references
    Q11089
    Defining formula
    B s ⁢ ( ξ ) subscript 𝐵 𝑠 𝜉 {\displaystyle{\displaystyle B_{s}(\xi)}}
    xml-id
    C2.S8.XMD24.m1bdec
    0 references
    Q11071
    Defining formula
    ψ ⁢ ( ξ ) 𝜓 𝜉 {\displaystyle{\displaystyle\psi(\xi)}}
    xml-id
    C2.S8.XMD7.m1idec
    0 references
     
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