Formula:334

Digital Library of Mathematical Functions ID 1.10.E9

${\displaystyle{\displaystyle N-P=\frac{1}{2\pi i}\int_{C}\frac{f^{\prime}(z)}{f(z)}\mathrm{d}z=\frac{1}{2\pi}\Delta_{C}(\operatorname{ph}f(z)),}}$

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle z}}$: variable
• ${\displaystyle{\displaystyle C}}$: closed contour
• ${\displaystyle{\displaystyle N}}$: number of zeros
• ${\displaystyle{\displaystyle P}}$: number of zeros
 

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