DLMF:9.9.E20 (Q2881): Difference between revisions

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Property / Symbols defined
 
Property / Symbols defined: expansion (locally) / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q10931 / rank
 
Normal rank
Property / Symbols used: Q10931 / qualifier
 
Defining formula:

∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}

\asympexp
Property / Symbols used: Q10931 / qualifier
 
xml-id: C2.S1.SS3.p1.m11abdec
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.m2apdec

Latest revision as of 14:43, 2 January 2020

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DLMF:9.9.E20
No description defined

    Statements

    Defining formula
    V ⁢ ( t ) ∼ π - 1 / 2 ⁢ t 1 / 6 ⁢ ( 1 + 5 48 ⁢ t - 2 - 1525 4608 ⁢ t - 4 + 23 97875 6 63552 ⁢ t - 6 - 7 48989 40625 8918 13888 ⁢ t - 8 + 14419 83037 34375 4 28070 66624 ⁢ t - 10 - ⋯ ) , asymptotic-expansion 𝑉 𝑡 superscript 𝜋 1 2 superscript 𝑡 1 6 1 5 48 superscript 𝑡 2 1525 4608 superscript 𝑡 4 23 97875 6 63552 superscript 𝑡 6 7 48989 40625 8918 13888 superscript 𝑡 8 14419 83037 34375 4 28070 66624 superscript 𝑡 10 ⋯ {\displaystyle{\displaystyle V(t)\sim\pi^{-1/2}t^{1/6}\left(1+\frac{5}{48}t^{-% 2}-\frac{1525}{4608}t^{-4}+\frac{23\;97875}{6\;63552}t^{-6}-\frac{7\;48989\;40% 625}{8918\;13888}t^{-8}+\frac{14419\;83037\;34375}{4\;28070\;66624}t^{-10}-% \cdots\right),}}
    0 references
    DLMF id
    DLMF:9.9.E20
    0 references
    Symbols used
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2apdec
    0 references
     
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