DLMF:29.14.E10 (Q8744)

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DLMF:29.14.E10
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    Statements

    Defining formula
    𝑠𝑐𝑑𝐸 2 ⁒ n + 3 m ⁑ ( s , k 2 ) ⁒ 𝑠𝑐𝑑𝐸 2 ⁒ n + 3 m ⁑ ( K ⁑ + i ⁒ t , k 2 ) . Lame-polynomial-scdE π‘š 2 𝑛 3 𝑠 superscript π‘˜ 2 Lame-polynomial-scdE π‘š 2 𝑛 3 complete-elliptic-integral-first-kind-K π‘˜ imaginary-unit 𝑑 superscript π‘˜ 2 {\displaystyle{\displaystyle\mathit{scdE}^{m}_{2n+3}\left(s,k^{2}\right)% \mathit{scdE}^{m}_{2n+3}\left(K+\mathrm{i}t,k^{2}\right).}}
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    DLMF id
    DLMF:29.14.E10
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    Symbols used
    LamΓ© polynomial
    Defining formula
    𝑠𝑐𝑑𝐸 2 ⁒ n + 3 m ⁑ ( z , k 2 ) Lame-polynomial-scdE π‘š 2 𝑛 3 𝑧 superscript π‘˜ 2 {\displaystyle{\displaystyle\mathit{scdE}^{\NVar{m}}_{2\NVar{n}+3}\left(\NVar{% z},\NVar{k^{2}}\right)}}
    xml-id
    C29.S12.E8.m2adec
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    Q11600
    Defining formula
    K ⁑ ( k ) complete-elliptic-integral-first-kind-K π‘˜ {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m1aidec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2ahdec
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