DLMF:19.5.E5 (Q6134)

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DLMF:19.5.E5
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    Statements

    Defining formula
    q = exp ⁡ ( - π ⁢ K ′ ⁡ ( k ) / K ⁡ ( k ) ) = r + 8 ⁢ r 2 + 84 ⁢ r 3 + 992 ⁢ r 4 + ⋯ , 𝑞 𝜋 complementary-complete-elliptic-integral-first-kind-K 𝑘 complete-elliptic-integral-first-kind-K 𝑘 𝑟 8 superscript 𝑟 2 84 superscript 𝑟 3 992 superscript 𝑟 4 ⋯ {\displaystyle{\displaystyle q=\exp\left(-\pi{K^{\prime}}\left(k\right)/K\left% (k\right)\right)=r+8r^{2}+84r^{3}+992r^{4}+\cdots,}}
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    DLMF id
    DLMF:19.5.E5
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    constraint
    0 ≤ k ≤ 1 0 𝑘 1 {\displaystyle{\displaystyle 0\leq k\leq 1}}
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    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
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    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
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    Q11600
    Defining formula
    K ⁡ ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m1aadec
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    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
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    nome
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C22.S2.E1.m2adec
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    Q11808
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C19.S1.XMD5.m1ddec
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