DLMF:36.11.E4 (Q10679): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: real parameter / rank
 
Normal rank
Property / Symbols used: real parameter / qualifier
 
DLMF defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: real parameter / qualifier
 
xml-id: C36.S1.XMD9.m1dec

Revision as of 03:02, 22 December 2021

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DLMF:36.11.E4
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    Statements

    DLMF defining formula
    Ψ 3 ⁡ ( x , 0 , 0 ) = 2 ⁢ π ( 5 ⁢ | x | 3 ) 1 / 8 ⁢ { exp ⁡ ( - 2 ⁢ 2 ⁢ ( x / 5 ) 5 / 4 ) ⁢ ( cos ⁡ ( 2 ⁢ 2 ⁢ ( x / 5 ) 5 / 4 - 1 8 ⁢ π ) + o ⁡ ( 1 ) ) , x → + ∞ , cos ⁡ ( 4 ⁢ ( | x | / 5 ) 5 / 4 - 1 4 ⁢ π ) + o ⁡ ( 1 ) , x → - ∞ . canonical-integral 3 𝑥 0 0 2 𝜋 superscript 5 superscript 𝑥 3 1 8 cases 2 2 superscript 𝑥 5 5 4 2 2 superscript 𝑥 5 5 4 1 8 𝜋 little-o 1 → 𝑥 4 superscript 𝑥 5 5 4 1 4 𝜋 little-o 1 → 𝑥 {\displaystyle{\displaystyle\Psi_{3}\left(x,0,0\right)=\frac{\sqrt{2\pi}}{(5|x% |^{3})^{1/8}}\begin{cases}\exp\left(-2\sqrt{2}(\ifrac{x}{5})^{5/4}\right)\left% (\cos\left(2\sqrt{2}(\ifrac{x}{5})^{5/4}-\tfrac{1}{8}\pi\right)+o\left(1\right% )\right),&x\to+\infty,\\ \cos\left(4(\ifrac{|x|}{5})^{5/4}-\tfrac{1}{4}\pi\right)+o\left(1\right),&x\to% -\infty.\end{cases}}}
    0 references
    Symbols used
    canonical integral function
    DLMF defining formula
    Ψ K ⁡ ( 𝐱 ) canonical-integral 𝐾 𝐱 {\displaystyle{\displaystyle\Psi_{\NVar{K}}\left(\NVar{\mathbf{x}}\right)}}
    xml-id
    C36.S2.E4.m2abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    cosine function
    DLMF defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
    0 references
    exponential function
    DLMF defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2abdec
    0 references
    order less than
    DLMF defining formula
    o ⁡ ( x ) little-o 𝑥 {\displaystyle{\displaystyle o\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E2.m2abdec
    0 references
    real parameter
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C36.S1.XMD9.m1dec
    0 references

    Identifiers

     
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