81 citations · 484 across the 73 of their papers we have counts for
5 papers · 1 filter
A curious polynomial interpolation of Carlitz-Riordan's -ballot numbers
Frédéric Chapoton, Jiang Zeng
We study a polynomial sequence defined as a solution of a -difference equation. This sequence, evaluated at -integers, interpolates Carlitz-Riordan's -ballot nu…
Basic and bibasic identities related to divisor functions
Victor J. W. Guo, Jiang Zeng
Using basic hypergeometric functions and partial fraction decomposition we give a new kind of generalization of identities due to Uchimura, Dilcher, Van Hamme, Prodinger, and Chen-…
A one-parameter generalization of Pfaffians
Theresia Eisenkölbl, Masao Ishikawa, Jiang Zeng
In analogy to the definition of the lambda-determinant, we define a one-parameter deformation of the Dodgson condensation formula for Pfaffians. We prove that the resulting rationa…
Positivity properties of Jacobi-Stirling numbers and generalized Ramanujan polynomials
Zhicong Lin, Jiang Zeng
Generalizing recent results of Egge and Mongelli, we show that each diagonal sequence of the Jacobi-Stirling numbers $\js(n,k;z)$ and $\JS(n,k;z)$ is a Pólya frequency sequence if…
q-Differential equations for q-classical polynomials and q-Jacobi-Stirling numbers
Ana F. Loureiro, Jiang Zeng
We introduce, characterise and provide a combinatorial interpretation for the so-called -Jacobi-Stirling numbers. This study is motivated by their key role in the (reciprocal) e…