DLMF:19.9.E8 (Q6947)

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DLMF:19.9.E8
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    Statements

    DLMF defining formula
    k ′ < E ⁡ ( k ) K ⁡ ( k ) < ( 1 + k ′ 2 ) 2 . superscript 𝑘 ′ complete-elliptic-integral-second-kind-E 𝑘 complete-elliptic-integral-first-kind-K 𝑘 superscript 1 superscript 𝑘 ′ 2 2 {\displaystyle{\displaystyle k^{\prime}<\frac{E\left(k\right)}{K\left(k\right)% }<\left(\frac{1+k^{\prime}}{2}\right)^{2}.}}
    0 references
    Symbols used
    Legendre’s complete elliptic integral of the first kind
    DLMF defining formula
    K ⁡ ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m1afdec
    0 references
    Legendre’s complete elliptic integral of the second kind
    DLMF defining formula
    E ⁡ ( k ) complete-elliptic-integral-second-kind-E 𝑘 {\displaystyle{\displaystyle E\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m2addec
    0 references
    real or complex modulus
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C19.S1.XMD5.m1gdec
    0 references
    complementary modulus
    DLMF defining formula
    k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}
    xml-id
    C19.S1.XMD6.m1gdec
    0 references

    Identifiers

     
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