# Generating functions

Fancy counting

June 19, 2017 — June 19, 2017

combinatorics

count data

probability

statistics

I don’t have much to say apart from a couple of links and references I need from time to time.

But nor should I; simply download Herbert Wilf’s pellucid free textbook for all the possible introduction you could need.

Rolf Bardeli walks through some beautiful generating function application.

Later I would like to include notes on graph theory and neat count RV tricks based on generating functions. You can rapidly get into weird complex analysis when you consider asymptotics of these guys and get to find out why Cauchy’s integral formula and Lagrange’s Inversion Theorem were in your textbook.

## 1 References

Consul, P., and Shenton. 1972. “Use of Lagrange Expansion for Generating Discrete Generalized Probability Distributions.”

*SIAM Journal on Applied Mathematics*.
Consul, P. C., and Shenton. 1973. “Some Interesting Properties of Lagrangian Distributions.”

*Communications in Statistics*.
Janardan. 1984. “Moments of Certain Series Distributions and Their Applications.”

*SIAM Journal on Applied Mathematics*.
Mutafchiev. 1995. “Local Limit Approximations for Lagrangian Distributions.”

*Aequationes Mathematicae*.
Saichev, and Sornette. 2011. “Generating Functions and Stability Study of Multivariate Self-Excited Epidemic Processes.”

*arXiv:1101.5564 [Cond-Mat, Physics:physics]*.
Wilf. 1994.

*Generatingfunctionology*.