DLMF:19.8.E5 (Q6211): 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.m2aadec

Revision as of 13:42, 2 January 2020

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DLMF:19.8.E5
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    Statements

    Defining formula
    K ⁡ ( k ) = π 2 ⁢ M ⁡ ( 1 , k ′ ) , complete-elliptic-integral-first-kind-K 𝑘 𝜋 2 arithmetic-geometric-mean 1 superscript 𝑘 ′ {\displaystyle{\displaystyle K\left(k\right)=\frac{\pi}{2M\left(1,k^{\prime}% \right)},}}
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    DLMF id
    DLMF:19.8.E5
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    constraint
    - ∞ < k 2 < 1 superscript 𝑘 2 1 {\displaystyle{\displaystyle-\infty<k^{2}<1}}
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    Symbols used
    Q11826
    Defining formula
    M ⁡ ( a , g ) arithmetic-geometric-mean 𝑎 𝑔 {\displaystyle{\displaystyle M\left(\NVar{a},\NVar{g}\right)}}
    xml-id
    C19.S8.SS1.p1.m7aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
     
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