DLMF:19.9.E7 (Q6250): Difference between revisions

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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.m2addec

Revision as of 13:45, 2 January 2020

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DLMF:19.9.E7
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    Statements

    Defining formula
    ( 1 - 1 4 ⁢ k 2 ) - 1 / 2 < 4 π ⁢ k 2 ⁢ ( E ⁡ ( k ) - k ′ 2 ⁢ K ⁡ ( k ) ) < min ⁡ ( ( k ′ ) - 1 / 4 , 4 / π ) , superscript 1 1 4 superscript 𝑘 2 1 2 4 𝜋 superscript 𝑘 2 complete-elliptic-integral-second-kind-E 𝑘 superscript superscript 𝑘 ′ 2 complete-elliptic-integral-first-kind-K 𝑘 superscript superscript 𝑘 ′ 1 4 4 𝜋 {\displaystyle{\displaystyle(1-\tfrac{1}{4}k^{2})^{-1/2}<\frac{4}{\pi k^{2}}(E% \left(k\right)-{k^{\prime}}^{2}K\left(k\right))<\min((k^{\prime})^{-1/4},4/\pi% ),}}
    0 references
    DLMF id
    DLMF:19.9.E7
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
     
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