DLMF:2.5.E35 (Q811)

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DLMF:2.5.E35
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    Statements

    Defining formula
    I j ⁢ k ⁢ ( x ) = ∑ p j ⁢ k < ℜ ⁡ z < q j ⁢ k res ⁡ [ - x - z ⁢ G j ⁢ k ⁢ ( z ) ] + E j ⁢ k ⁢ ( x ) , subscript 𝐼 𝑗 𝑘 𝑥 subscript subscript 𝑝 𝑗 𝑘 𝑧 subscript 𝑞 𝑗 𝑘 residue delimited-[] superscript 𝑥 𝑧 subscript 𝐺 𝑗 𝑘 𝑧 subscript 𝐸 𝑗 𝑘 𝑥 {\displaystyle{\displaystyle I_{jk}(x)=\sum_{p_{jk}<\Re z<q_{jk}}\Residue\left% [-x^{-z}G_{jk}(z)\right]+E_{jk}(x),}}
    0 references
    DLMF id
    DLMF:2.5.E35
    0 references
    Symbols used
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1aedec
    0 references
    Q10960
    Defining formula
    res residue {\displaystyle{\displaystyle\Residue}}
    xml-id
    C1.S10.SS3.p5.m4abdec
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    Q11010
    Defining formula
    G j ⁢ k ⁢ ( z ) subscript 𝐺 𝑗 𝑘 𝑧 {\displaystyle{\displaystyle G_{jk}(z)}}
    xml-id
    C2.S5.XMD21.m1cdec
    0 references
    Q11011
    Defining formula
    p j ⁢ k subscript 𝑝 𝑗 𝑘 {\displaystyle{\displaystyle p_{jk}}}
    xml-id
    C2.S5.XMD22.m1bdec
    0 references
    Q11012
    Defining formula
    q j ⁢ k > p j ⁢ k subscript 𝑞 𝑗 𝑘 subscript 𝑝 𝑗 𝑘 {\displaystyle{\displaystyle q_{jk}>p_{jk}}}
    xml-id
    C2.S5.XMD23.m1adec
    0 references
    Q11013
    Defining formula
    E j ⁢ k ⁢ ( x ) subscript 𝐸 𝑗 𝑘 𝑥 {\displaystyle{\displaystyle E_{jk}(x)}}
    xml-id
    C2.S5.XMD24.m1dec
    0 references
     
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