Formula:4110

Digital Library of Mathematical Functions ID 10.22.E39

${\displaystyle{\displaystyle\int_{x}^{\infty}\frac{J_{0}\left(t\right)}{t}\mathrm{d}t+\gamma+\ln\left(\tfrac{1}{2}x\right)=\int_{0}^{x}\frac{1-J_{0}\left(t\right)}{t}\mathrm{d}t=\sum_{k=1}^{\infty}(-1)^{k-1}\frac{(\frac{1}{2}x)^{2k}}{2k(k!)^{2}},}}$

Symbols List

• ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the first kind
• ${\displaystyle{\displaystyle\gamma}}$: Euler’s constant
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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