Formula:3524

Digital Library of Mathematical Functions ID 9.7.E17

${\displaystyle{\displaystyle\begin{cases}1,&|\operatorname{ph}z|\leq\tfrac{1}{3}\pi,\\ \min\left(|\csc\left(\operatorname{ph}\zeta\right)|,\chi(n+\sigma)+1\right),&\tfrac{1}{3}\pi\leq|\operatorname{ph}z|\leq\tfrac{2}{3}\pi,\\ \frac{\sqrt{2\pi(n+\sigma)}}{|\cos\left(\operatorname{ph}\zeta\right)|^{n+\sigma}}+\chi(n+\sigma)+1,&\tfrac{2}{3}\pi\leq|\operatorname{ph}z|<\pi,\end{cases}}}$

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\csc\NVar{z}}}$: cosecant function
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\exp\NVar{z}}}$: exponential function
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\zeta}}$: change of variable (locally)
• ${\displaystyle{\displaystyle\chi(x)}}$: function (locally)
• ${\displaystyle{\displaystyle n}}$: index
• ${\displaystyle{\displaystyle\sigma}}$: real variable
 

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