DLMF:20.4.E3 (Q6757): Difference between revisions

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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 14:31, 2 January 2020

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DLMF:20.4.E3
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    Statements

    Defining formula
    θ 2 ⁡ ( 0 , q ) = 2 ⁢ q 1 / 4 ⁢ ∏ n = 1 ∞ ( 1 - q 2 ⁢ n ) ⁢ ( 1 + q 2 ⁢ n ) 2 , Jacobi-theta 2 0 𝑞 2 superscript 𝑞 1 4 superscript subscript product 𝑛 1 1 superscript 𝑞 2 𝑛 superscript 1 superscript 𝑞 2 𝑛 2 {\displaystyle{\displaystyle\theta_{2}\left(0,q\right)=2q^{1/4}\prod\limits_{n% =1}^{\infty}\left(1-q^{2n}\right)\left(1+q^{2n}\right)^{2},}}
    0 references
    DLMF id
    DLMF:20.4.E3
    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
    Q11947
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C20.S1.XMD2.m1adec
    0 references
    Q11950
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C20.S1.XMD5.m1bdec
    0 references
     
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