If-I-n-denotes-z-n-e-1-z-dz-then-show-that-n-1-I-n-I-0-e-1-z-1-z-2-2-z-3-n-z-n-1-

Question Number 202592 by Calculusboy last updated on 30/Dec/23

I f I_{n} d e n o t e s \int z^{n} e^{\frac{1}{z}} d z, t h e n s h o w t h a t

(n + 1)! I_{n} = I_{0} + e^{\frac{1}{z}} (1 \cdot! z^{2} + 2 \cdot! z^{3} + \cdot \cdot \cdot + n! \cdot z^{n + 1})