Formula:7549

Digital Library of Mathematical Functions ID 20.13.E4

${\displaystyle{\displaystyle\sqrt{\frac{\pi}{4\alpha t}}\sum\limits_{n=-\infty}^{\infty}e^{-(n\pi+z)^{2}/(4\alpha t)}=\theta_{3}\left(z\middle|i4\alpha t/\pi\right),}}$

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
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle n}}$: integer
• ${\displaystyle{\displaystyle t}}$: time
• ${\displaystyle{\displaystyle\alpha}}$: real parameter
• ${\displaystyle{\displaystyle z}}$: real variable
 

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