Formula:4317

Digital Library of Mathematical Functions ID 10.43.E6

${\displaystyle{\displaystyle\int_{0}^{x}e^{-t}I_{n}\left(t\right)\mathrm{d}t=xe^{-x}(I_{0}\left(x\right)+I_{1}\left(x\right))+n(e^{-x}I_{0}\left(x\right)-1)+2e^{-x}\sum_{k=1}^{n-1}(n-k)I_{k}\left(x\right),}}$

Constraint(s)

${\displaystyle{\displaystyle n=0,1,2,\ldots}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}$: modified Bessel function of the first kind
• ${\displaystyle{\displaystyle n}}$: integer
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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