DLMF:23.8.E7 (Q7289): Difference between revisions

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Property / Symbols used: DLMF:23.2.E6 / rank
 
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Property / Symbols used: DLMF:23.2.E6 / qualifier
 
Defining formula:

σ ( z ) Weierstrass-sigma-on-lattice 𝑧 𝕃 {\displaystyle{\displaystyle\sigma\left(\NVar{z}\right)}}

\Weierstrasssigmalatt@@{\NVar{z}}{\NVar{\mathbb{L}}}
Property / Symbols used: DLMF:23.2.E6 / qualifier
 
xml-id: C23.S2.E6.m2aadec

Revision as of 15:56, 2 January 2020

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DLMF:23.8.E7
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    Statements

    σ ( z ) = 2 ω 1 π exp ( η 1 z 2 2 ω 1 ) sin ( π z 2 ω 1 ) n = 1 sin ( π ( 2 n ω 3 + z ) / ( 2 ω 1 ) ) sin ( π ( 2 n ω 3 - z ) / ( 2 ω 1 ) ) sin 2 ( π n ω 3 / ω 1 ) . Weierstrass-sigma-on-lattice 𝑧 𝕃 2 subscript 𝜔 1 𝜋 subscript 𝜂 1 superscript 𝑧 2 2 subscript 𝜔 1 𝜋 𝑧 2 subscript 𝜔 1 superscript subscript product 𝑛 1 𝜋 2 𝑛 subscript 𝜔 3 𝑧 2 subscript 𝜔 1 𝜋 2 𝑛 subscript 𝜔 3 𝑧 2 subscript 𝜔 1 2 𝜋 𝑛 subscript 𝜔 3 subscript 𝜔 1 {\displaystyle{\displaystyle\sigma\left(z\right)=\frac{2\omega_{1}}{\pi}\exp% \left(\frac{\eta_{1}z^{2}}{2\omega_{1}}\right)\sin\left(\frac{\pi z}{2\omega_{% 1}}\right)\prod_{n=1}^{\infty}\frac{\sin\left(\pi(2n\omega_{3}+z)/(2\omega_{1}% )\right)\sin\left(\pi(2n\omega_{3}-z)/(2\omega_{1})\right)}{{\sin^{2}}\left(% \pi n\omega_{3}/\omega_{1}\right)}.}}
    0 references
    DLMF:23.8.E7
    0 references
    σ ( z ) Weierstrass-sigma-on-lattice 𝑧 𝕃 {\displaystyle{\displaystyle\sigma\left(\NVar{z}\right)}}
    C23.S2.E6.m2aadec
    0 references