DLMF:29.15.E46 (Q8791)

From DRMF
Revision as of 01:37, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:29.15.E46
No description defined

    Statements

    Defining formula
    𝑑𝐸 2 ⁢ n + 1 m ⁡ ( z , k 2 ) = dn ⁡ ( z , k ) ⁢ ( 1 2 ⁢ C 0 + ∑ p = 1 n C 2 ⁢ p ⁢ T 2 ⁢ p ⁡ ( sn ⁡ ( z , k ) ) ) , Lame-polynomial-dE 𝑚 2 𝑛 1 𝑧 superscript 𝑘 2 Jacobi-elliptic-dn 𝑧 𝑘 1 2 subscript 𝐶 0 superscript subscript 𝑝 1 𝑛 subscript 𝐶 2 𝑝 Chebyshev-polynomial-first-kind-T 2 𝑝 Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\mathit{dE}^{m}_{2n+1}\left(z,k^{2}\right)=% \operatorname{dn}\left(z,k\right)\left(\tfrac{1}{2}C_{0}+\sum_{p=1}^{n}C_{2p}T% _{2p}\left(\operatorname{sn}\left(z,k\right)\right)\right),}}
    0 references
    DLMF id
    DLMF:29.15.E46
    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.m2abdec
    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.m2addec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q8791&oldid=33061"