DLMF:10.38.E3

MaRDI QIDQ4259

• Label: DLMF:10.38.E3

Digital Library of Mathematical Functions ID 10.38.E3

${\displaystyle{\displaystyle\left.(-1)^{n}\frac{\partial I_{\nu}\left(z\right)}{\partial\nu}\right|_{\nu=n}=-K_{n}\left(z\right)+\frac{n!}{2(\frac{1}{2}z)^{n}}\sum_{k=0}^{n-1}(-1)^{k}\frac{(\frac{1}{2}z)^{k}I_{k}\left(z\right)}{k!(n-k)},}}$

Symbols List

• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}$: modified Bessel function of the first kind
• ${\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}$: modified Bessel function of the second kind
• ${\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}$: partial derivative of $$f$$ with respect to $$x$$
• ${\displaystyle{\displaystyle\partial\NVar{x}}}$: partial differential of $$x$$
• ${\displaystyle{\displaystyle n}}$: integer
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

Resources that cite this formula

No records found.