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DLMF:29.14.E11 - MaRDI portal

DLMF:29.14.E11 (Q9437)

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DLMF:29.14.E11
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    Statements

    DLMF defining formula
    ⟨ g , h ⟩ = ∫ 0 4 ⁢ K ⁡ ∫ 0 2 ⁢ K ′ ⁡ w ⁢ ( s , t ) ⁢ g ⁢ ( s , t ) ⁢ h ⁢ ( s , t ) ⁢ d t ⁢ d s , 𝑔 ℎ superscript subscript 0 4 complete-elliptic-integral-first-kind-K 𝑘 superscript subscript 0 2 complementary-complete-elliptic-integral-first-kind-K 𝑘 𝑤 𝑠 𝑡 𝑔 𝑠 𝑡 ℎ 𝑠 𝑡 𝑡 𝑠 {\displaystyle{\displaystyle\langle g,h\rangle=\int_{0}^{4K}\!\!\int_{0}^{2{K^% {\prime}}}w(s,t)g(s,t)h(s,t)\mathrm{d}t\mathrm{d}s,}}
    0 references
    Symbols used
    Legendre’s complementary complete elliptic integral of the first kind
    DLMF 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.m1aadec
    0 references
    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.m1ajdec
    0 references
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
    0 references
    real parameter
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C29.S1.XMD8.m1jdec
    0 references
    function
    DLMF defining formula
    w ⁢ ( s , t ) 𝑤 𝑠 𝑡 {\displaystyle{\displaystyle w(s,t)}}
    xml-id
    C29.S14.XMD2.m1bdec
    0 references

    Identifiers

     
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