DLMF:2.6.E7 (Q832): 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.m2abdec

Revision as of 17:10, 1 January 2020

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DLMF:2.6.E7
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    Statements

    Defining formula
    S ⁢ ( x ) ∼ 2 ⁢ π 3 ⁢ ∑ s = 0 ∞ ( - 1 ) s ⁢ ( - 1 3 s ) ⁢ x - s - ( 1 / 3 ) - ∑ s = 1 ∞ 3 s ⁢ ( s - 1 ) ! 2 ⋅ 5 ⁢ ⋯ ⁢ ( 3 ⁢ s - 1 ) ⁢ x - s ; asymptotic-expansion 𝑆 𝑥 2 𝜋 3 superscript subscript 𝑠 0 superscript 1 𝑠 binomial 1 3 𝑠 superscript 𝑥 𝑠 1 3 superscript subscript 𝑠 1 superscript 3 𝑠 𝑠 1 ⋅ 2 5 ⋯ 3 𝑠 1 superscript 𝑥 𝑠 {\displaystyle{\displaystyle S(x)\sim\frac{2\pi}{\sqrt{3}}\sum_{s=0}^{\infty}(% -1)^{s}{\genfrac{(}{)}{0.0pt}{}{-\frac{1}{3}}{s}}x^{-s-(1/3)}-\sum_{s=1}^{% \infty}\frac{3^{s}(s-1)!}{2\cdot 5\cdots(3s-1)}x^{-s};}}
    0 references
    DLMF id
    DLMF:2.6.E7
    0 references
    Symbols used
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11aadec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1abdec
    0 references
    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
     
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