We consider positive powers of a rational generating function F(x, z) of the variable z whose numerator has degree at most 1, denominator has degree 2, and where coefficients are functions of x. Many ...

1. Introduction The probability generating function approach plays a vital role in the study of queueing problems as it is crucially useful in performance analysis of a wide range of queueing models.

Finally, the relationship between the generating function method and the Karlin-McGregor approach based on orthogonal polynomial theory is established. SIAM Journal on Applied Mathematics contains ...

Prodinger, H. (2021) Convolution Identities for Tribonacci Numbers via the Diagonal of a Bivariate Generating Function. Palestine Journal of Mathematics, 10, 440-442.

This is a course covering a number of concepts and techniques of discrete mathematics. Topics covered: Counting: selections; inclusion-exclusion; generating functions; recurrence relations.

According to the idea of adaptive subdivision, a backward recursive method based on the universal generating function is suggested for structural reliability calculation.