Formula:8365

Digital Library of Mathematical Functions ID 25.10.E2

${\displaystyle{\displaystyle\vartheta(t)\equiv\operatorname{ph}\Gamma\left(\tfrac{1}{4}+\tfrac{1}{2}it\right)-\tfrac{1}{2}t\ln\pi}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\overline{\NVar{z}}}}$: complex conjugate
• ${\displaystyle{\displaystyle\equiv}}$:
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\vartheta(t)}}$: function
• ${\displaystyle{\displaystyle\chi(s)}}$:
 

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