DLMF:19.9.E4 (Q6247): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11808 / rank
 
Normal rank
Property / Symbols used: Q11808 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11808 / qualifier
 
xml-id: C19.S1.XMD5.m1cdec

Revision as of 13:44, 2 January 2020

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DLMF:19.9.E4
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    Statements

    Defining formula
    ( 1 + k ′ 3 / 2 2 ) 2 / 3 ≤ 2 π ⁢ E ⁡ ( k ) ≤ ( 1 + k ′ 2 2 ) 1 / 2 superscript 1 superscript superscript 𝑘 ′ 3 2 2 2 3 2 𝜋 complete-elliptic-integral-second-kind-E 𝑘 superscript 1 superscript superscript 𝑘 ′ 2 2 1 2 {\displaystyle{\displaystyle\left(\frac{1+{k^{\prime}}^{3/2}}{2}\right)^{2/3}% \leq\frac{2}{\pi}E\left(k\right)\leq\left(\frac{1+{k^{\prime}}^{2}}{2}\right)^% {1/2}}}
    0 references
    DLMF id
    DLMF:19.9.E4
    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.m2aadec
    0 references
    Q11601
    Defining formula
    E ⁡ ( k ) complete-elliptic-integral-second-kind-E 𝑘 {\displaystyle{\displaystyle E\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m2aadec
    0 references
    Q11808
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C19.S1.XMD5.m1cdec
    0 references
     
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