DLMF:23.6.E12 (Q7253): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q12049 / rank
 
Normal rank
Property / Symbols used: Q12049 / qualifier
 
Defining formula:

ω 1 subscript 𝜔 1 {\displaystyle{\displaystyle\omega_{1}}}

\omega_{1}
Property / Symbols used: Q12049 / qualifier
 
xml-id: C23.S1.XMD8.m1kdec

Revision as of 15:48, 2 January 2020

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DLMF:23.6.E12
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    Statements

    σ ( ω 3 ) = - 2 ω 1 exp ( 1 2 η 1 ω 1 ) θ 4 ( 0 , q ) π q 1 / 4 θ 1 ( 0 , q ) . Weierstrass-sigma-on-lattice subscript 𝜔 3 𝕃 2 subscript 𝜔 1 1 2 subscript 𝜂 1 subscript 𝜔 1 Jacobi-theta 4 0 𝑞 𝜋 superscript 𝑞 1 4 diffop Jacobi-theta 1 1 0 𝑞 {\displaystyle{\displaystyle\sigma\left(\omega_{3}\right)=-2\omega_{1}\frac{% \exp\left(\tfrac{1}{2}\eta_{1}\omega_{1}\right)\theta_{4}\left(0,q\right)}{\pi q% ^{1/4}\theta_{1}'\left(0,q\right)}.}}
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    DLMF:23.6.E12
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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.m2ajdec
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    σ ( z ) Weierstrass-sigma-on-lattice 𝑧 𝕃 {\displaystyle{\displaystyle\sigma\left(\NVar{z}\right)}}
    C23.S2.E6.m2acdec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2akdec
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    exp z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    C4.S2.E19.m2acdec
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    𝕃 𝕃 {\displaystyle{\displaystyle\mathbb{L}}}
    C23.S1.XMD1.m1idec
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    q 𝑞 {\displaystyle{\displaystyle q}}
    C23.S1.XMD10.m1kdec
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    ω 1 subscript 𝜔 1 {\displaystyle{\displaystyle\omega_{1}}}
    C23.S1.XMD8.m1kdec
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