Formula:3411

Digital Library of Mathematical Functions ID 8.19.E27

${\displaystyle{\displaystyle L(p)=\int_{0}^{\infty}e^{-t}E_{p}\left(t\right)\mathrm{d}t=\frac{1}{2p}F\left(1,1;1+p;\tfrac{1}{2}\right),}}$

Constraint(s)

${\displaystyle{\displaystyle p>0}}$

Symbols List

• ${\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle E_{\NVar{p}}\left(\NVar{z}\right)}}$: generalized exponential integral
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle p}}$: parameter
• ${\displaystyle{\displaystyle L(p)}}$: function
 

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