指数積分
E i r e a l  ( x ) = lim ε → + 0 ( − ∫ − x − ε e − t t d t − ∫ ε ∞ e − t t d t ) ( x > 0 ) E i r e a l  ( x ) = − ∫ − x ∞ e − t t d t ( x < 0 ) {\displaystyle {\begin{aligned}\operatorname {{Ei}^{real}} (x)&=\lim _{\epsilon \to +0}\left(-\int _{-x}^{-\epsilon }{\frac {e^{-t}}{t}}\,\operatorname {d} \!t-\int _{\epsilon }^{\infty }{\frac {e^{-t}}{t}}\,\operatorname {d} \!t\right)\quad &(x>0)\\\operatorname {{Ei}^{real}} (x)&=-\int _{-x}^{\infty }{\frac {e^{-t}}{t}}\,\operatorname {d} \!t\quad &(x<0)\end{aligned}}}