DLMF:36.8.E4 (Q9948)

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DLMF:36.8.E4
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    Statements

    Defining formula
    Ψ ( E ) ⁡ ( 𝐱 ) = 2 ⁢ π 2 ⁢ ( 2 3 ) 2 / 3 ⁢ ∑ n = 0 ∞ ( - i ⁢ ( 2 / 3 ) 2 / 3 ⁢ z ) n n ! ⁢ ℜ ⁡ ( f n ⁢ ( x + i ⁢ y 12 1 / 3 , x - i ⁢ y 12 1 / 3 ) ) , elliptic-umbilic-canonical-integral 𝐱 2 superscript 𝜋 2 superscript 2 3 2 3 superscript subscript 𝑛 0 superscript 𝑖 superscript 2 3 2 3 𝑧 𝑛 𝑛 subscript 𝑓 𝑛 𝑥 𝑖 𝑦 superscript 12 1 3 𝑥 𝑖 𝑦 superscript 12 1 3 {\displaystyle{\displaystyle\Psi^{(\mathrm{E})}\left(\mathbf{x}\right)=2\pi^{2% }\left(\dfrac{2}{3}\right)^{2/3}\sum\limits_{n=0}^{\infty}\dfrac{\left(-i(2/3)% ^{2/3}z\right)^{n}}{n!}\Re\left(f_{n}\left(\dfrac{x+iy}{12^{1/3}},\dfrac{x-iy}% {12^{1/3}}\right)\right),}}
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    DLMF id
    DLMF:36.8.E4
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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.m2abdec
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    elliptic umbilic canonical integral function
    Defining formula
    Ψ ( E ) ⁡ ( 𝐱 ) elliptic-umbilic-canonical-integral 𝐱 {\displaystyle{\displaystyle\Psi^{(\mathrm{E})}\left(\NVar{\mathbf{x}}\right)}}
    xml-id
    C36.S2.E5.m3adec
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