DLMF:20.11.E8 (Q6849): Difference between revisions

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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.m5abdec
Property / Symbols used
 
Property / Symbols used: Q11951 / rank
 
Normal rank
Property / Symbols used: Q11951 / qualifier
 
Defining formula:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q11951 / qualifier
 
xml-id: C20.S1.XMD1.m1cdec
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.m1ddec
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.m1cdec
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.m1bdec

Latest revision as of 14:44, 2 January 2020

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DLMF:20.11.E8
No description defined

    Statements

    Defining formula
    φ m , n ⁡ ( z , q ) = θ n ⁡ ( 0 , q ) ⁢ θ m ⁡ ( z , q ) θ m ⁡ ( 0 , q ) ⁢ θ n ⁡ ( z , q ) , Jacobi-theta-combined 𝑚 𝑛 𝑧 𝑞 Jacobi-theta 𝑛 0 𝑞 Jacobi-theta 𝑚 𝑧 𝑞 Jacobi-theta 𝑚 0 𝑞 Jacobi-theta 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\varphi_{m,n}\left(z,q\right)=\frac{\theta_{n}% \left(0,q\right)\theta_{m}\left(z,q\right)}{\theta_{m}\left(0,q\right)\theta_{% n}\left(z,q\right)},}}
    0 references
    DLMF id
    DLMF:20.11.E8
    0 references
    constraint
    m , n = 2 , 3 , 4 formulae-sequence 𝑚 𝑛 2 3 4 {\displaystyle{\displaystyle m,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.m2abdec
    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.m5abdec
    0 references
    Q11951
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C20.S1.XMD1.m1cdec
    0 references
    Q11947
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C20.S1.XMD2.m1ddec
    0 references
    Q11948
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C20.S1.XMD3.m1cdec
    0 references
    Q11950
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C20.S1.XMD5.m1bdec
    0 references
     
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