DLMF:19.5.E10 (Q6139)

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DLMF:19.5.E10
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    Statements

    Defining formula
    K ⁡ ( k ) = π 2 ⁢ ∏ m = 1 ∞ ( 1 + k m ) , complete-elliptic-integral-first-kind-K 𝑘 𝜋 2 superscript subscript product 𝑚 1 1 subscript 𝑘 𝑚 {\displaystyle{\displaystyle K\left(k\right)=\frac{\pi}{2}\prod_{m=1}^{\infty}% (1+k_{m}),}}
    0 references
    DLMF id
    DLMF:19.5.E10
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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.m2agdec
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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.m1addec
    0 references
    Q11818
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C19.S1.XMD2.m1ddec
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    Q11808
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C19.S1.XMD5.m1hdec
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