DLMF:29.15.E43 (Q8788): Difference between revisions

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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.m1tdec

Revision as of 01:36, 2 January 2020

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DLMF:29.15.E43
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    Statements

    Defining formula
    𝑢𝐸 2 ⁢ n m ⁡ ( z , k 2 ) = 1 2 ⁢ A 0 + ∑ p = 1 n A 2 ⁢ p ⁢ T 2 ⁢ p ⁡ ( sn ⁡ ( z , k ) ) . Lame-polynomial-uE 𝑚 2 𝑛 𝑧 superscript 𝑘 2 1 2 subscript 𝐴 0 superscript subscript 𝑝 1 𝑛 subscript 𝐴 2 𝑝 Chebyshev-polynomial-first-kind-T 2 𝑝 Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\mathit{uE}^{m}_{2n}\left(z,k^{2}\right)=\tfrac{1}% {2}A_{0}+\sum_{p=1}^{n}A_{2p}T_{2p}\left(\operatorname{sn}\left(z,k\right)% \right).}}
    0 references
    DLMF id
    DLMF:29.15.E43
    0 references
    Symbols used
    Q11207
    Defining formula
    T n ⁡ ( x ) Chebyshev-polynomial-first-kind-T 𝑛 𝑥 {\displaystyle{\displaystyle T_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r4.m2adec
    0 references
    Jacobian elliptic function
    Defining formula
    sn ⁡ ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E4.m2adec
    0 references
    Lamé polynomial
    Defining formula
    𝑢𝐸 2 ⁢ n m ⁡ ( z , k 2 ) Lame-polynomial-uE 𝑚 2 𝑛 𝑧 superscript 𝑘 2 {\displaystyle{\displaystyle\mathit{uE}^{\NVar{m}}_{2\NVar{n}}\left(\NVar{z},% \NVar{k^{2}}\right)}}
    xml-id
    C29.S12.E1.m2aadec
    0 references
    Q12357
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C29.S1.XMD1.m1pdec
    0 references
    Q12367
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C29.S1.XMD2.m1ahdec
    0 references
    Q12359
    Defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C29.S1.XMD3.m1xdec
    0 references
    Q12348
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C29.S1.XMD6.m1hdec
    0 references
    Q12350
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C29.S1.XMD8.m1tdec
    0 references
     
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