Tag Archives: Bell numbers

How to solve this differential equation?

How would you solve the differential equation with the initial condition ? I know what the answer is supposed to be, but I don’t know how to directly solve it. In case you’re wondering, is the exponential generating function for … Continue reading

Posted in combinatorics, math | Tagged , , , , | 15 Comments

The Poisson distribution and Stirling numbers

While working on an assignment for my machine learning class, I rediscovered the fact that if X is a random variable from a Poisson distribution with parameter , then where denotes a Stirling number of the second kind. (I actually … Continue reading

Posted in combinatorics, grad school, learning, math | Tagged , , , | 2 Comments