DLMF:36.9.E3 (Q9956): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1abdec

Revision as of 15:11, 2 January 2020

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DLMF:36.9.E3
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    Statements

    Defining formula
    | Ψ 1 ⁡ ( x ) | 2 = 8 ⁢ π 3 ⁢ ∫ 0 ∞ u - 1 / 2 ⁢ cos ⁡ ( 2 ⁢ u ⁢ ( x + u 2 ) + 1 4 ⁢ π ) ⁢ d u . superscript canonical-integral 1 𝑥 2 8 𝜋 3 superscript subscript 0 superscript 𝑢 1 2 2 𝑢 𝑥 superscript 𝑢 2 1 4 𝜋 𝑢 {\displaystyle{\displaystyle|\Psi_{1}\left(x\right)|^{2}=\sqrt{\frac{8\pi}{3}}% \int_{0}^{\infty}u^{-1/2}\cos\left(2u(x+u^{2})+\tfrac{1}{4}\pi\right)\mathrm{d% }u.}}
    0 references
    DLMF id
    DLMF:36.9.E3
    0 references
    Symbols used
    canonical integral function
    Defining formula
    Ψ K ⁡ ( 𝐱 ) canonical-integral 𝐾 𝐱 {\displaystyle{\displaystyle\Psi_{\NVar{K}}\left(\NVar{\mathbf{x}}\right)}}
    xml-id
    C36.S2.E4.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
     
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