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

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2ahdec

Revision as of 14:40, 2 January 2020

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DLMF:9.8.E20
No description defined

    Statements

    Defining formula
    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}},}}
    0 references
    DLMF id
    DLMF:9.8.E20
    0 references
    Symbols used
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ahdec
    0 references
     
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