Formula:7520

Digital Library of Mathematical Functions ID 20.7.E30

${\displaystyle{\displaystyle(-i\tau)^{1/2}\theta_{1}\left(z\middle|\tau\right)=-i\exp\left(i\tau^{\prime}z^{2}/\pi\right)\theta_{1}\left(z\tau^{\prime}\middle|\tau^{\prime}\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z}\middle|\NVar{\tau}\right)}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\exp\NVar{z}}}$: exponential function
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle z}}$: complex
• ${\displaystyle{\displaystyle\tau}}$: lattice parameter
 

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