DLMF:20.11.E7 (Q6848): Difference between revisions

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Property / constraint
 

n = 2 , 3 , 4 𝑛 2 3 4 {\displaystyle{\displaystyle n=2,3,4}}

n=2,3,4
Property / constraint: n = 2 , 3 , 4 𝑛 2 3 4 {\displaystyle{\displaystyle n=2,3,4}} / 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.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11955 / rank
 
Normal rank
Property / Symbols used: Q11955 / qualifier
 
Defining formula:

φ n , m ⁡ ( z , q ) Jacobi-theta-combined 𝑛 𝑚 𝑧 𝑞 {\displaystyle{\displaystyle\varphi_{\NVar{n},\NVar{m}}\left(\NVar{z},\NVar{q}% \right)}}

\Jacobithetacombinedq{\NVar{n}}{\NVar{m}}@{\NVar{z}}{\NVar{q}}
Property / Symbols used: Q11955 / qualifier
 
xml-id: C20.S11.SS5.p2.m5aadec
Property / Symbols used
 
Property / Symbols used: Q11947 / rank
 
Normal rank
Property / Symbols used: Q11947 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11947 / qualifier
 
xml-id: C20.S1.XMD2.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11948 / rank
 
Normal rank
Property / Symbols used: Q11948 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11948 / qualifier
 
xml-id: C20.S1.XMD3.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11950 / rank
 
Normal rank
Property / Symbols used: Q11950 / qualifier
 
Defining formula:

q 𝑞 {\displaystyle{\displaystyle q}}

q
Property / Symbols used: Q11950 / qualifier
 
xml-id: C20.S1.XMD5.m1adec

Latest revision as of 14:44, 2 January 2020

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DLMF:20.11.E7
No description defined

    Statements

    Defining formula
    φ 1 , n ⁡ ( z , q ) = θ n ⁡ ( 0 , q ) ⁢ θ 1 ⁡ ( z , q ) θ 1 ′ ⁡ ( 0 , q ) ⁢ θ n ⁡ ( z , q ) , Jacobi-theta-combined 1 𝑛 𝑧 𝑞 Jacobi-theta 𝑛 0 𝑞 Jacobi-theta 1 𝑧 𝑞 diffop Jacobi-theta 1 1 0 𝑞 Jacobi-theta 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\varphi_{1,n}\left(z,q\right)=\frac{\theta_{n}% \left(0,q\right)\theta_{1}\left(z,q\right)}{\theta_{1}'\left(0,q\right)\theta_% {n}\left(z,q\right)},}}
    0 references
    DLMF id
    DLMF:20.11.E7
    0 references
    constraint
    n = 2 , 3 , 4 𝑛 2 3 4 {\displaystyle{\displaystyle n=2,3,4}}
    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.m2aadec
    0 references
    Q11955
    Defining formula
    φ n , m ⁡ ( z , q ) Jacobi-theta-combined 𝑛 𝑚 𝑧 𝑞 {\displaystyle{\displaystyle\varphi_{\NVar{n},\NVar{m}}\left(\NVar{z},\NVar{q}% \right)}}
    xml-id
    C20.S11.SS5.p2.m5aadec
    0 references
    Q11947
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C20.S1.XMD2.m1cdec
    0 references
    Q11948
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C20.S1.XMD3.m1bdec
    0 references
    Q11950
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C20.S1.XMD5.m1adec
    0 references
     
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