DLMF:9.8.E20 (Q2855): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
Defining formula:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5adec
Property / Symbols used
 
Property / Symbols used: Airy modulus function / rank
 
Normal rank
Property / Symbols used: Airy modulus function / qualifier
 
Defining formula:

M ( z ) modulus-Airy-M 𝑧 {\displaystyle{\displaystyle M\left(\NVar{z}\right)}}

\AirymodM@{\NVar{z}}
Property / Symbols used: Airy modulus function / qualifier
 
xml-id: C9.S8.E3.m2ajdec
Property / Symbols used
 
Property / Symbols used: Q11382 / rank
 
Normal rank
Property / Symbols used: Q11382 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11382 / qualifier
 
xml-id: C9.S1.XMD2.m1sdec

Latest revision as of 14:40, 2 January 2020

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DLMF:9.8.E20
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    Statements

    M 2 ( x ) 1 π ( - x ) 1 / 2 k = 0 1 3 5 ( 6 k - 1 ) k ! ( 96 ) k 1 x 3 k , asymptotic-expansion modulus-Airy-M 2 𝑥 1 𝜋 superscript 𝑥 1 2 superscript subscript 𝑘 0 1 3 5 6 𝑘 1 𝑘 superscript 96 𝑘 1 superscript 𝑥 3 𝑘 {\displaystyle{\displaystyle{M^{2}}\left(x\right)\sim\frac{1}{\pi(-x)^{1/2}}% \sum_{k=0}^{\infty}\frac{1\cdot 3\cdot 5\cdots(6k-1)}{k!(96)^{k}}\frac{1}{x^{3% k}},}}
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    DLMF:9.8.E20
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    asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    C2.S1.SS3.p1.m11adec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2ahdec
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    ! {\displaystyle{\displaystyle!}}
    introduction.Sx4.p1.t1.r15.m5adec
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    M ( z ) modulus-Airy-M 𝑧 {\displaystyle{\displaystyle M\left(\NVar{z}\right)}}
    C9.S8.E3.m2ajdec
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    x 𝑥 {\displaystyle{\displaystyle x}}
    C9.S1.XMD2.m1sdec
    0 references