DLMF:19.9.E5 (Q6248): 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.m1ddec

Revision as of 13:44, 2 January 2020

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DLMF:19.9.E5
No description defined

    Statements

    Defining formula
    ln ⁡ ( 1 + k ′ ) 2 k < π ⁢ K ′ ⁡ ( k ) 2 ⁢ K ⁡ ( k ) < ln ⁡ 2 ⁢ ( 1 + k ′ ) k . superscript 1 superscript 𝑘 ′ 2 𝑘 𝜋 complementary-complete-elliptic-integral-first-kind-K 𝑘 2 complete-elliptic-integral-first-kind-K 𝑘 2 1 superscript 𝑘 ′ 𝑘 {\displaystyle{\displaystyle\ln\frac{(1+\sqrt{k^{\prime}})^{2}}{k}<\frac{\pi{K% ^{\prime}}\left(k\right)}{2K\left(k\right)}<\ln\frac{2(1+k^{\prime})}{k}.}}
    0 references
    DLMF id
    DLMF:19.9.E5
    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.m2abdec
    0 references
    Q11821
    Defining formula
    K ′ ⁡ ( k ) complementary-complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle{K^{\prime}}\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E9.m1adec
    0 references
    Q11600
    Defining formula
    K ⁡ ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m1acdec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2acdec
    0 references
    Q11808
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C19.S1.XMD5.m1ddec
    0 references
     
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