DLMF:10.43.E30

MaRDI QIDQ4341

• Label: DLMF:10.43.E30

Digital Library of Mathematical Functions ID 10.43.E30

${\displaystyle{\displaystyle f(y)=\frac{2y}{\pi^{2}}\sinh\left(\pi y\right)\int_{0}^{\infty}\frac{g(x)}{x}K_{iy}\left(x\right)\mathrm{d}x.}}$

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
• ${\displaystyle{\displaystyle\sinh\NVar{z}}}$: hyperbolic sine function
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}$: modified Bessel function of the second kind
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle y}}$: real variable
• ${\displaystyle{\displaystyle g(x)}}$: function
 

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