DLMF:19.7.E1 (Q6181)

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DLMF:19.7.E1
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    Statements

    Defining formula
    E ⁡ ( k ) ⁢ K ′ ⁡ ( k ) + E ′ ⁡ ( k ) ⁢ K ⁡ ( k ) - K ⁡ ( k ) ⁢ K ′ ⁡ ( k ) = 1 2 ⁢ π . complete-elliptic-integral-second-kind-E 𝑘 complementary-complete-elliptic-integral-first-kind-K 𝑘 complementary-complete-elliptic-integral-second-kind-E 𝑘 complete-elliptic-integral-first-kind-K 𝑘 complete-elliptic-integral-first-kind-K 𝑘 complementary-complete-elliptic-integral-first-kind-K 𝑘 1 2 𝜋 {\displaystyle{\displaystyle E\left(k\right){K^{\prime}}\left(k\right)+{E^{% \prime}}\left(k\right)K\left(k\right)-K\left(k\right){K^{\prime}}\left(k\right% )=\tfrac{1}{2}\pi.}}
    0 references
    DLMF id
    DLMF:19.7.E1
    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.m2adec
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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
    0 references
     
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