Formula:8018

Digital Library of Mathematical Functions ID 23.12.E3

${\displaystyle{\displaystyle\sigma\left(z\right)=\frac{2\omega_{1}}{\pi}\exp\left(\frac{\pi^{2}z^{2}}{24\omega_{1}^{2}}\right)\sin\left(\frac{\pi z}{2\omega_{1}}\right)\*\left(1-\left(\frac{\pi^{2}z^{2}}{\omega_{1}^{2}}-4{\sin^{2}}\left(\frac{\pi z}{2\omega_{1}}\right)\right)q^{2}+O\left(q^{4}\right)\right),}}$

Symbols List

• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle\sigma\left(\NVar{z}\right)}}$: 23.2.E6
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\exp\NVar{z}}}$: exponential function
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle\mathbb{L}}}$: lattice
• ${\displaystyle{\displaystyle q}}$: nome
• ${\displaystyle{\displaystyle z}}$: complex
• ${\displaystyle{\displaystyle\omega_{1}}}$: lattice generators
 

Resources that cite this formula

No records found.