DLMF:6.4.E3

MaRDI QIDQ2934

• Label: DLMF:6.4.E3

Digital Library of Mathematical Functions ID 6.4.E3

${\displaystyle{\displaystyle E_{1}\left(ze^{\pm\pi i}\right)=\mathrm{Ein}\left(-z\right)-\ln z-\gamma\mp\pi i,}}$

Constraint(s)

${\displaystyle{\displaystyle|\operatorname{ph}z|\leq\pi}}$

Symbols List

• ${\displaystyle{\displaystyle\gamma}}$: Euler’s constant
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{Ein}\left(\NVar{z}\right)}}$: complementary exponential integral
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle E_{1}\left(\NVar{z}\right)}}$: exponential integral
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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