DLMF:36.8.E4 (Q9948): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: function (locally) / rank
 
Normal rank
Property / Symbols used: function (locally) / qualifier
 
Defining formula:

f n subscript 𝑓 𝑛 {\displaystyle{\displaystyle f_{n}}}

f_{n}
Property / Symbols used: function (locally) / qualifier
 
xml-id: C36.S8.XMD2.m1dec

Latest revision as of 15:11, 2 January 2020

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English
DLMF:36.8.E4
No description defined

    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),}}
    0 references
    DLMF id
    DLMF:36.8.E4
    0 references
    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
    0 references
    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
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1adec
    0 references
    Q12745
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C36.S1.XMD10.m1adec
    0 references
    Q12746
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C36.S1.XMD11.m1adec
    0 references
    Q12755
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C36.S1.XMD3.m1cdec
    0 references
    Q12748
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C36.S1.XMD9.m1adec
    0 references
    function (locally)
    Defining formula
    f n subscript 𝑓 𝑛 {\displaystyle{\displaystyle f_{n}}}
    xml-id
    C36.S8.XMD2.m1dec
    0 references
     
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