DLMF:29.15.E44 (Q8789): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q12350 / rank
 
Normal rank
Property / Symbols used: Q12350 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12350 / qualifier
 
xml-id: C29.S1.XMD8.m1udec

Revision as of 01:36, 2 January 2020

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DLMF:29.15.E44
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    Statements

    𝑠𝐸 2 n + 1 m ( z , k 2 ) = p = 0 n A 2 p + 1 T 2 p + 1 ( sn ( z , k ) ) , Lame-polynomial-sE 𝑚 2 𝑛 1 𝑧 superscript 𝑘 2 superscript subscript 𝑝 0 𝑛 subscript 𝐴 2 𝑝 1 Chebyshev-polynomial-first-kind-T 2 𝑝 1 Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\mathit{sE}^{m}_{2n+1}\left(z,k^{2}\right)=\sum_{p% =0}^{n}A_{2p+1}T_{2p+1}\left(\operatorname{sn}\left(z,k\right)\right),}}
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    DLMF:29.15.E44
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    T n ( x ) Chebyshev-polynomial-first-kind-T 𝑛 𝑥 {\displaystyle{\displaystyle T_{\NVar{n}}\left(\NVar{x}\right)}}
    C18.S3.T1.t1.r4.m2aadec
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    sn ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E4.m2aadec
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    𝑠𝐸 2 n + 1 m ( z , k 2 ) Lame-polynomial-sE 𝑚 2 𝑛 1 𝑧 superscript 𝑘 2 {\displaystyle{\displaystyle\mathit{sE}^{\NVar{m}}_{2\NVar{n}+1}\left(\NVar{z}% ,\NVar{k^{2}}\right)}}
    C29.S12.E2.m2aadec
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    m 𝑚 {\displaystyle{\displaystyle m}}
    C29.S1.XMD1.m1qdec
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    n 𝑛 {\displaystyle{\displaystyle n}}
    C29.S1.XMD2.m1aidec
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    p 𝑝 {\displaystyle{\displaystyle p}}
    C29.S1.XMD3.m1ydec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C29.S1.XMD6.m1idec
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    k 𝑘 {\displaystyle{\displaystyle k}}
    C29.S1.XMD8.m1udec
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