Formula:4701

Digital Library of Mathematical Functions ID 11.7.E14

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

Symbols List

• ${\displaystyle{\displaystyle\mathbf{H}_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Struve function
• ${\displaystyle{\displaystyle\pi}}$: 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
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle a}}$: parameter
 

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