Formula:4285

Digital Library of Mathematical Functions ID 10.40.E10

${\displaystyle{\displaystyle K_{\nu}\left(z\right)=\left(\frac{\pi}{2z}\right)^{\frac{1}{2}}e^{-z}\left(\sum_{k=0}^{\ell-1}\frac{a_{k}(\nu)}{z^{k}}+R_{\ell}(\nu,z)\right),}}$

Constraint(s)

${\displaystyle{\displaystyle\ell=1,2,\ldots}}$

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}$: modified Bessel function of the second kind
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
• ${\displaystyle{\displaystyle a_{k}(\nu)}}$: expansion (locally)
• ${\displaystyle{\displaystyle R_{\ell}(\nu,z)}}$: remainder (locally)
 

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