All Questions
Tagged with bell-numbers exponential-function
2
questions
1
vote
0
answers
34
views
On deriving a 'simple' formula for the taylor series of $\exp^{f(x_1,x_2)}$
It is written explicitly in wikipedia, https://en.wikipedia.org/wiki/Bell_polynomials#Generating_function, how one obtains a simple analytic expression for the Taylor series of the exponential of a ...
- 31
2
votes
1
answer
98
views
Closed form for $H(n,k)=\frac{1}{k!}\sum_{j=0}^\infty H(n-k, j)j^k$ where $H(1,k)=\frac{1}{k!}$
Let $H(n,k)$ be defined such that
$$H(1,k)=\frac{1}{k!}\text{, and }H(n,k)=\frac{1}{k!}\sum_{j=0}^\infty H(n-1,j)j^k$$
As pointed out in the comments, I should mention that we must define $0^0=1$ as ...
- 4,472