DLMF:10.32.E5

MaRDI QIDQ4222

• Label: DLMF:10.32.E5

Digital Library of Mathematical Functions ID 10.32.E5

${\displaystyle{\displaystyle K_{0}\left(z\right)=-\frac{1}{\pi}\int_{0}^{\pi}e^{\pm z\cos\theta}\left(\gamma+\ln\left(2z(\sin\theta)^{2}\right)\right)\mathrm{d}\theta.}}$

Symbols List

• ${\displaystyle{\displaystyle\gamma}}$: Euler’s constant
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}$: modified Bessel function of the second kind
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle z}}$: complex variable
 

Resources that cite this formula

No records found.