DLMF:10.22.E45

MaRDI QIDQ4116

• Label: DLMF:10.22.E45

Digital Library of Mathematical Functions ID 10.22.E45

${\displaystyle{\displaystyle\int_{0}^{\infty}\frac{1-J_{0}\left(t\right)}{t^{\mu}}\mathrm{d}t=-\frac{\pi\sec\left(\frac{1}{2}\mu\pi\right)}{2^{\mu}{\Gamma^{2}}\left(\frac{1}{2}\mu+\frac{1}{2}\right)},}}$

Constraint(s)

${\displaystyle{\displaystyle 1<\Re\mu<3}}$

Symbols List

• ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the first kind
• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle\sec\NVar{z}}}$: secant function
 

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