DLMF:29.15.E50 (Q8795): Difference between revisions

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

𝑠𝑐𝑑𝐸 2 ⁢ n + 3 m ⁡ ( z , k 2 ) Lame-polynomial-scdE 𝑚 2 𝑛 3 𝑧 superscript 𝑘 2 {\displaystyle{\displaystyle\mathit{scdE}^{\NVar{m}}_{2\NVar{n}+3}\left(\NVar{% z},\NVar{k^{2}}\right)}}

\LamepolyscdE{\NVar{m}}{2\NVar{n}+3}@{\NVar{z}}{\NVar{k^{2}}}
Property / Symbols used: Lamé polynomial / qualifier
 
xml-id: C29.S12.E8.m2aadec

Revision as of 01:38, 2 January 2020

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DLMF:29.15.E50
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    Statements

    Defining formula
    𝑠𝑐𝑑𝐸 2 ⁢ n + 3 m ⁡ ( z , k 2 ) = cn ⁡ ( z , k ) ⁢ dn ⁡ ( z , k ) ⁢ ∑ p = 0 n D 2 ⁢ p + 2 ⁢ U 2 ⁢ p + 1 ⁡ ( sn ⁡ ( z , k ) ) . Lame-polynomial-scdE 𝑚 2 𝑛 3 𝑧 superscript 𝑘 2 Jacobi-elliptic-cn 𝑧 𝑘 Jacobi-elliptic-dn 𝑧 𝑘 superscript subscript 𝑝 0 𝑛 subscript 𝐷 2 𝑝 2 Chebyshev-polynomial-second-kind-U 2 𝑝 1 Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\mathit{scdE}^{m}_{2n+3}\left(z,k^{2}\right)=% \operatorname{cn}\left(z,k\right)\operatorname{dn}\left(z,k\right)\sum_{p=0}^{% n}D_{2p+2}U_{2p+1}\left(\operatorname{sn}\left(z,k\right)\right).}}
    0 references
    DLMF id
    DLMF:29.15.E50
    0 references
    Symbols used
    Q11661
    Defining formula
    U n ⁡ ( x ) Chebyshev-polynomial-second-kind-U 𝑛 𝑥 {\displaystyle{\displaystyle U_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r5.m2acdec
    0 references
    Jacobian elliptic function
    Defining formula
    cn ⁡ ( z , k ) Jacobi-elliptic-cn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E5.m2acdec
    0 references
    Jacobian elliptic function
    Defining formula
    dn ⁡ ( z , k ) Jacobi-elliptic-dn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E6.m2agdec
    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.m2agdec
    0 references
    Lamé polynomial
    Defining formula
    𝑠𝑐𝑑𝐸 2 ⁢ n + 3 m ⁡ ( z , k 2 ) Lame-polynomial-scdE 𝑚 2 𝑛 3 𝑧 superscript 𝑘 2 {\displaystyle{\displaystyle\mathit{scdE}^{\NVar{m}}_{2\NVar{n}+3}\left(\NVar{% z},\NVar{k^{2}}\right)}}
    xml-id
    C29.S12.E8.m2aadec
    0 references
     
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