Formula:4702

Digital Library of Mathematical Functions ID 11.7.E15

${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-at}\mathbf{L}_{0}\left(t\right)\mathrm{d}t=\frac{2}{\pi\sqrt{a^{2}\!-\!1}}\operatorname{arcsin}\left(\frac{1}{a}\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\operatorname{arcsin}\NVar{z}}}$:
• ${\displaystyle{\displaystyle\mathbf{L}_{\NVar{\nu}}\left(\NVar{z}\right)}}$: modified Struve function
• ${\displaystyle{\displaystyle a}}$: parameter
 

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