Formula:2981

Digital Library of Mathematical Functions ID 6.10.E6

${\displaystyle{\displaystyle\mathrm{Ei}\left(x\right)=\gamma+\ln\left|x\right|+\sum_{n=0}^{\infty}(-1)^{n}(x-a_{n})\left({\mathsf{i}^{(1)}_{n}}\left(\tfrac{1}{2}x\right)\right)^{2},}}$

Constraint(s)

${\displaystyle{\displaystyle x\neq 0}}$

Symbols List

• ${\displaystyle{\displaystyle\gamma}}$: Euler’s constant
• ${\displaystyle{\displaystyle\mathrm{Ei}\left(\NVar{x}\right)}}$:
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle{\mathsf{i}^{(1)}_{\NVar{n}}}\left(\NVar{z}\right)}}$: modified spherical Bessel function
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle a_{n}}}$: coefficients (locally)
 

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