DLMF:29.14.E5 (Q8739)

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DLMF:29.14.E5
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    Statements

    Defining formula
    𝑐𝐸 2 ⁒ n + 1 m ⁑ ( s , k 2 ) ⁒ 𝑐𝐸 2 ⁒ n + 1 m ⁑ ( K ⁑ + i ⁒ t , k 2 ) , Lame-polynomial-cE π‘š 2 𝑛 1 𝑠 superscript π‘˜ 2 Lame-polynomial-cE π‘š 2 𝑛 1 complete-elliptic-integral-first-kind-K π‘˜ imaginary-unit 𝑑 superscript π‘˜ 2 {\displaystyle{\displaystyle\mathit{cE}^{m}_{2n+1}\left(s,k^{2}\right)\mathit{% cE}^{m}_{2n+1}\left(K+\mathrm{i}t,k^{2}\right),}}
    0 references
    DLMF id
    DLMF:29.14.E5
    0 references
    Symbols used
    LamΓ© polynomial
    Defining formula
    𝑐𝐸 2 ⁒ n + 1 m ⁑ ( z , k 2 ) Lame-polynomial-cE π‘š 2 𝑛 1 𝑧 superscript π‘˜ 2 {\displaystyle{\displaystyle\mathit{cE}^{\NVar{m}}_{2\NVar{n}+1}\left(\NVar{z}% ,\NVar{k^{2}}\right)}}
    xml-id
    C29.S12.E3.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.m1addec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
    0 references
    Q12357
    Defining formula
    m π‘š {\displaystyle{\displaystyle m}}
    xml-id
    C29.S1.XMD1.m1bdec
    0 references
     
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