Formula:8531

Digital Library of Mathematical Functions ID 26.8.E13

${\displaystyle{\displaystyle\sum_{n,k=0}^{\infty}S\left(n,k\right)\frac{x^{n}}{n!}y^{k}=\exp\left(y({\mathrm{e}^{x}}-1)\right).}}$

Symbols List

• ${\displaystyle{\displaystyle S\left(\NVar{n},\NVar{k}\right)}}$:
• ${\displaystyle{\displaystyle\exp\NVar{z}}}$: exponential function
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

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