DLMF:20.4.E10 (Q6765): Difference between revisions

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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.m2aidec

Revision as of 14:31, 2 January 2020

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DLMF:20.4.E10
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    θ 3 ′′ ( 0 , q ) θ 3 ( 0 , q ) = - 8 n = 1 q 2 n - 1 ( 1 + q 2 n - 1 ) 2 , diffop Jacobi-theta 3 2 0 𝑞 Jacobi-theta 3 0 𝑞 8 superscript subscript 𝑛 1 superscript 𝑞 2 𝑛 1 superscript 1 superscript 𝑞 2 𝑛 1 2 {\displaystyle{\displaystyle\frac{\theta_{3}''\left(0,q\right)}{\theta_{3}% \left(0,q\right)}=-8\sum_{n=1}^{\infty}\frac{q^{2n-1}}{(1+q^{2n-1})^{2}},}}
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    DLMF:20.4.E10
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    θ j ( z , q ) Jacobi-theta 𝑗 𝑧 𝑞 {\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z},\NVar{q}\right)}}
    C20.S2.SS1.m2aidec
    0 references