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

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‎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

    Defining formula
    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)}.}}
    0 references
    DLMF id
    DLMF:23.6.E12
    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.m2ajdec
    0 references
    DLMF:23.2.E6
    Defining formula
    σ ⁡ ( z ) Weierstrass-sigma-on-lattice 𝑧 𝕃 {\displaystyle{\displaystyle\sigma\left(\NVar{z}\right)}}
    xml-id
    C23.S2.E6.m2acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2akdec
    0 references
    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2acdec
    0 references
    Q12055
    Defining formula
    𝕃 𝕃 {\displaystyle{\displaystyle\mathbb{L}}}
    xml-id
    C23.S1.XMD1.m1idec
    0 references
    Q12066
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C23.S1.XMD10.m1kdec
    0 references
    Q12049
    Defining formula
    ω 1 subscript 𝜔 1 {\displaystyle{\displaystyle\omega_{1}}}
    xml-id
    C23.S1.XMD8.m1kdec
    0 references
     
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