DLMF:29.14.E1 (Q8735)

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DLMF:29.14.E1
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    Statements

    Defining formula
    f n m ⁒ ( s , t ) = 𝑒𝐸 2 ⁒ n m ⁑ ( s , k 2 ) ⁒ 𝑒𝐸 2 ⁒ n m ⁑ ( K ⁑ + i ⁒ t , k 2 ) , superscript subscript 𝑓 𝑛 π‘š 𝑠 𝑑 Lame-polynomial-uE π‘š 2 𝑛 𝑠 superscript π‘˜ 2 Lame-polynomial-uE π‘š 2 𝑛 complete-elliptic-integral-first-kind-K π‘˜ imaginary-unit 𝑑 superscript π‘˜ 2 {\displaystyle{\displaystyle f_{n}^{m}(s,t)=\mathit{uE}^{m}_{2n}\left(s,k^{2}% \right)\mathit{uE}^{m}_{2n}\left(K+\mathrm{i}t,k^{2}\right),}}
    0 references
    DLMF id
    DLMF:29.14.E1
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    constraint
    m = 0 , 1 , … , n π‘š 0 1 … 𝑛 {\displaystyle{\displaystyle m=0,1,\dots,n}}
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    Symbols used
    LamΓ© polynomial
    Defining formula
    𝑒𝐸 2 ⁒ n m ⁑ ( z , k 2 ) Lame-polynomial-uE π‘š 2 𝑛 𝑧 superscript π‘˜ 2 {\displaystyle{\displaystyle\mathit{uE}^{\NVar{m}}_{2\NVar{n}}\left(\NVar{z},% \NVar{k^{2}}\right)}}
    xml-id
    C29.S12.E1.m2adec
    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.m1adec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
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    Q12357
    Defining formula
    m π‘š {\displaystyle{\displaystyle m}}
    xml-id
    C29.S1.XMD1.m1dec
    0 references
     
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