Formula:10151

Digital Library of Mathematical Functions ID 32.11.E24

${\displaystyle{\displaystyle s=\left(\exp\left(\pi d^{2}\right)-1\right)^{1/2}\*\exp\left(i\left(\tfrac{3}{2}d^{2}\ln 2-\tfrac{1}{4}\pi+\chi-\operatorname{ph}\Gamma\left(\tfrac{1}{2}id^{2}\right)\right)\right).}}$

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
• ${\displaystyle{\displaystyle\exp\NVar{z}}}$: exponential function
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle\chi}}$: constant
• ${\displaystyle{\displaystyle d}}$: constant
 

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