arXiv subjects

Diane Yahui Shi

Publications and source records attributed to Diane Yahui Shi.

2 recordsLinked to original sources

arXiv2018

Orthogonal Polynomials and Lattice Path Interpretation for Higher-order Euler Polynomials

We study the higher-order Euler polynomials and give the corresponding monic orthogonal polynomials, which are Meixner-Pollaczek polynomials with certain arguments and constant factors. Moreover, through a general connection between moments of random variables and the generalized Motzkin numbers, we can obtain a new recurrence formula and a matrix representation for the higher-order Euler polynomials, interpreting them as weighted lattice paths.

math.CO↗

arXiv2017

Matrix Representation for Multiplicative Nested Sums

We study multiplicative nested sums, which are generalizations of harmonic sums, and provide a calculation through multiplication of index matrices. Special cases interpret the index matrices as stochastic transition matrices of random walks on a finite number of sites. Relations among multiplicative nested sums, which are generalizations of relations between harmonic series and multiple zeta functions, can be easily derived from identities of the index matrices. Combinatorial identities and their generalizations can also be derived from this computation.

math.CO↗