DLMF:19.32.E2 (Q6692)

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DLMF:19.32.E2
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    Statements

    Defining formula
    d z = - 1 2 ⁢ ( ∏ j = 1 3 ( p - x j ) - 1 / 2 ) ⁢ d p , 𝑧 1 2 superscript subscript product 𝑗 1 3 superscript 𝑝 subscript 𝑥 𝑗 1 2 𝑝 {\displaystyle{\displaystyle\mathrm{d}z=-\frac{1}{2}\left(\prod_{j=1}^{3}(p-x_% {j})^{-1/2}\right)\mathrm{d}p,}}
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    DLMF id
    DLMF:19.32.E2
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    constraint
    ℑ ⁡ p > 0 𝑝 0 {\displaystyle{\displaystyle\Im p>0}}
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    0 < ph ⁡ ( p - x j ) < π 0 phase 𝑝 subscript 𝑥 𝑗 𝜋 {\displaystyle{\displaystyle 0<\operatorname{ph}\left(p-x_{j}\right)<\pi}}
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    ℑ ⁡ p > 0 𝑝 0 {\displaystyle{\displaystyle\Im p>0}}
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    0 < ph ⁡ ( p - x j ) < π 0 ph 𝑝 subscript 𝑥 𝑗 𝜋 {\displaystyle{\displaystyle 0<\operatorname{ph}\left(p-x_{j}\right)<\pi}}
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    j = 1 , 2 , 3 𝑗 1 2 3 {\displaystyle{\displaystyle j=1,2,3}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
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    Q10901
    Defining formula
    ℑ ⁡ absent {\displaystyle{\displaystyle\Im}}
    xml-id
    C1.S9.E2.m2adec
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