DLMF:29.8.E5 (Q8709)

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DLMF:29.8.E5
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    Statements

    Defining formula
    𝐸𝑐 Ξ½ 2 ⁒ m ⁑ ( z 1 , k 2 ) ⁒ w 2 ⁒ ( K ⁑ ) - w 2 ⁒ ( - K ⁑ ) d w 2 ⁒ ( z ) / d z | z = 0 = ∫ - K ⁑ K ⁑ 𝖯 Ξ½ ⁑ ( y ) ⁒ 𝐸𝑐 Ξ½ 2 ⁒ m ⁑ ( z , k 2 ) ⁒ d z , Lame-Ec 2 π‘š 𝜈 subscript 𝑧 1 superscript π‘˜ 2 subscript 𝑀 2 complete-elliptic-integral-first-kind-K π‘˜ subscript 𝑀 2 complete-elliptic-integral-first-kind-K π‘˜ evaluated-at derivative subscript 𝑀 2 𝑧 𝑧 𝑧 0 superscript subscript complete-elliptic-integral-first-kind-K π‘˜ complete-elliptic-integral-first-kind-K π‘˜ shorthand-Ferrers-Legendre-P-first-kind 𝜈 𝑦 Lame-Ec 2 π‘š 𝜈 𝑧 superscript π‘˜ 2 𝑧 {\displaystyle{\displaystyle\mathit{Ec}^{2m}_{\nu}\left(z_{1},k^{2}\right)% \frac{w_{2}(K)-w_{2}(-K)}{\left.\ifrac{\mathrm{d}w_{2}(z)}{\mathrm{d}z}\right|% _{z=0}}=\int_{-K}^{K}\mathsf{P}_{\nu}\left(y\right)\mathit{Ec}^{2m}_{\nu}\left% (z,k^{2}\right)\mathrm{d}z,}}
    0 references
    DLMF id
    DLMF:29.8.E5
    0 references
    Symbols used
    Q12362
    Defining formula
    𝐸𝑐 Ξ½ m ⁑ ( z , k 2 ) Lame-Ec π‘š 𝜈 𝑧 superscript π‘˜ 2 {\displaystyle{\displaystyle\mathit{Ec}^{\NVar{m}}_{\NVar{\nu}}\left(\NVar{z},% \NVar{k^{2}}\right)}}
    xml-id
    C29.S3.SS4.p1.m5adec
    0 references
    Q11600
    Defining formula
    K ⁑ ( k ) complete-elliptic-integral-first-kind-K π‘˜ {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m1abdec
    0 references
     
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