Results 41 to 50 of about 19,306,633 (313)

On the exponential generating function for non-backtracking walks

Linear Algebra and its Applications, 2018
We derive an explicit formula for the exponential generating function associated with non-backtracking walks around a graph. We study both undirected and directed graphs. Our results allow us to derive computable expressions for non-backtracking versions
F. Arrigo, P. Grindrod, D. Higham, V. Noferini   +3 more
semanticscholar   +1 more source

Hybrid Numbers with Fibonacci and Lucas Hybrid Number Coefficients

Universal Journal of Mathematics and Applications, 2023
In this paper, we introduce hybrid numbers with Fibonacci and Lucas hybrid number coefficients. We give the Binet formulas, generating functions, and exponential generating functions for these numbers. Then we define an associate matrix for these numbers.
Emrah Polatlı
doaj   +1 more source

A generating function approach to branching random walks [PDF]

, 2015
It is well known that the behaviour of a branching process is completely described by the generating function of the offspring law and its fixed points.
D. Bertacchi, F. Zucca
semanticscholar   +1 more source

Generating-function method for fusion rules

, 2000
This is the second of two articles devoted to an exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper focuses on fusion rules, using the machinery developed for tensor products in the companion
Berenstein A. D., Berenstein A. D., Bégin L., Bégin L., Bégin L., C. Cummins, Couture M., Cummins C. J., Cummins C. J., Fuchs J., Kirillov A. N., L. Bégin, Mathieu P., P. Mathieu, Sharp R. T., Stanley R. P., Verlinde E., Walton M., Walton M. A., Walton M. A.   +19 more
core   +2 more sources

Some identities of bivariate Pell and bivariate Pell-Lucas polynomials

Journal of Amasya University the Institute of Sciences and Technology, 2023
In this paper, we obtain some identities for the bivariate Pell polynomials and bivariate Pell-Lucas polynomials. We establish some sums and connection formulas involving them.
Yashwant Panwar
doaj   +1 more source

Generating-function method for tensor products

, 2000
This is the first of two articles devoted to a exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper is entirely devoted to the study of the tensor-product (infinite-level) limit of fusions ...
Berenstein A. D., Berenstein A. D., Bégin L., Bégin L., C. Cummins, Couture M., Cummins C. J., Elliott E. B., Huet G., L. Bégin, P. Mathieu, Sharp R. T., Stanley R. P.   +12 more
core   +2 more sources

A Short Note on Integral Transformations and Conversion Formulas for Sequence Generating Functions

Axioms, 2019
The purpose of this note is to provide an expository introduction to some more curious integral formulas and transformations involving generating functions.
Maxie D. Schmidt
doaj   +1 more source

Performance Analysis of Generating Function Approach for Optimal Reconfiguration of Formation Flying [PDF]

Journal of Astronomy and Space Sciences, 2013
The use of generating functions for solving optimal rendezvous problems has an advantage in the sense that it does not require one to guess and iterate the initial costate.
Kwangwon Lee, Chandeok Park, Sang-Young Park   +2 more
doaj   +1 more source

A comparative study on generating function relations for generalized hypergeometric functions via generalized fractional operators

, 2018
In this paper, we present further generalizations of the beta function; Riemann–Liouville, Caputo and Kober–Erdelyi fractional operators by using confluent hypergeometric function with six parameters.
A. Çetinkaya, I. O. Kiymaz, P. Agarwal, R. Agarwal   +3 more
semanticscholar   +1 more source

Connections between discriminants and the root distribution of polynomials with rational generating function [PDF]

, 2014
Let H m ( z ) be a sequence of polynomials whose generating function ∑ m = 0 ∞ H m ( z ) t m is the reciprocal of a bivariate polynomial D ( t , z ) . We show that in the three cases D ( t , z ) = 1 + B ( z ) t + A ( z ) t 2 , D ( t , z ) = 1 + B ( z ) t
Khang Tran
semanticscholar   +1 more source