DLMF:22.2.E5 (Q6927): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11985 / rank
 
Normal rank
Property / Symbols used: Q11985 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11985 / qualifier
 
xml-id: C22.S1.XMD3.m1bdec

Revision as of 14:55, 2 January 2020

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DLMF:22.2.E5
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    Statements

    Defining formula
    cn ⁡ ( z , k ) = θ 4 ⁡ ( 0 , q ) θ 2 ⁡ ( 0 , q ) ⁢ θ 2 ⁡ ( ζ , q ) θ 4 ⁡ ( ζ , q ) = 1 nc ⁡ ( z , k ) , Jacobi-elliptic-cn 𝑧 𝑘 Jacobi-theta 4 0 𝑞 Jacobi-theta 2 0 𝑞 Jacobi-theta 2 𝜁 𝑞 Jacobi-theta 4 𝜁 𝑞 1 Jacobi-elliptic-nc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cn}\left(z,k\right)=\frac{\theta_{4}% \left(0,q\right)}{\theta_{2}\left(0,q\right)}\frac{\theta_{2}\left(\zeta,q% \right)}{\theta_{4}\left(\zeta,q\right)}=\frac{1}{\operatorname{nc}\left(z,k% \right)},}}
    0 references
    DLMF id
    DLMF:22.2.E5
    0 references
    Symbols used
    Q11945
    Defining formula
    θ j ⁡ ( z , q ) Jacobi-theta 𝑗 𝑧 𝑞 {\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z},\NVar{q}\right)}}
    xml-id
    C20.S2.SS1.m2abdec
    0 references
    nome
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C22.S2.E1.m2acdec
    0 references
    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1bdec
    0 references
     
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