DLMF:22.2.E9 (Q6931): Difference between revisions

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Property / Symbols defined
 
Property / Symbols defined: Jacobian elliptic function / rank
 
Normal rank
Property / Symbols defined
 
Property / Symbols defined: Jacobian elliptic function / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q11945 / rank
 
Normal rank
Property / Symbols used: Q11945 / qualifier
 
Defining formula:

θ j ⁡ ( z , q ) Jacobi-theta 𝑗 𝑧 𝑞 {\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z},\NVar{q}\right)}}

\Jacobithetaq{\NVar{j}}@{\NVar{z}}{\NVar{q}}
Property / Symbols used: Q11945 / qualifier
 
xml-id: C20.S2.SS1.m2afdec
Property / Symbols used
 
Property / Symbols used: nome / rank
 
Normal rank
Property / Symbols used: nome / qualifier
 
Defining formula:

q 𝑞 {\displaystyle{\displaystyle q}}

q
Property / Symbols used: nome / qualifier
 
xml-id: C22.S2.E1.m2agdec
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.m1fdec
Property / Symbols used
 
Property / Symbols used: Q11984 / rank
 
Normal rank
Property / Symbols used: Q11984 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11984 / qualifier
 
xml-id: C22.S1.XMD4.m1hdec
Property / Symbols used
 
Property / Symbols used: Q11986 / rank
 
Normal rank
Property / Symbols used: Q11986 / qualifier
 
Defining formula:

ζ 𝜁 {\displaystyle{\displaystyle\zeta}}

\zeta
Property / Symbols used: Q11986 / qualifier
 
xml-id: C22.S2.XMD2.m1fdec

Latest revision as of 14:55, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:22.2.E9
No description defined

    Statements

    Defining formula
    sc ⁡ ( z , k ) = θ 3 ⁡ ( 0 , q ) θ 4 ⁡ ( 0 , q ) ⁢ θ 1 ⁡ ( ζ , q ) θ 2 ⁡ ( ζ , q ) = 1 cs ⁡ ( z , k ) . Jacobi-elliptic-sc 𝑧 𝑘 Jacobi-theta 3 0 𝑞 Jacobi-theta 4 0 𝑞 Jacobi-theta 1 𝜁 𝑞 Jacobi-theta 2 𝜁 𝑞 1 Jacobi-elliptic-cs 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sc}\left(z,k\right)=\frac{\theta_{3}% \left(0,q\right)}{\theta_{4}\left(0,q\right)}\frac{\theta_{1}\left(\zeta,q% \right)}{\theta_{2}\left(\zeta,q\right)}=\frac{1}{\operatorname{cs}\left(z,k% \right)}.}}
    0 references
    DLMF id
    DLMF:22.2.E9
    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.m2afdec
    0 references
    nome
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C22.S2.E1.m2agdec
    0 references
    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1fdec
    0 references
    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1hdec
    0 references
    Q11986
    Defining formula
    ζ 𝜁 {\displaystyle{\displaystyle\zeta}}
    xml-id
    C22.S2.XMD2.m1fdec
    0 references
     
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