6 citations · 22 across the 25 of their papers we have counts for
5 papers · 1 filter
Refinements of the Bell and Stirling numbers
Tanay Wakhare
We introduce new refinements of the Bell, factorial, and unsigned Stirling numbers of the first and second kind that unite the derangement, involution, associated factorial, associ…
Some generating functions for q-polynomials
Howard S. Cohl, Roberto S. Costas-Santos, Tanay V. Wakhare
We obtain q-analogues of the Sylvester, Cesàro, Pasternack, and Bateman polynomials. We also derive generating functions for these polynomials.
A continuous analogue of lattice path enumeration
T. Wakhare, C. Vignat, Q. -N. Le +1
Following the work of Cano and Diaz, we consider a continuous analog of lattice path enumeration. This allows us to define a continuous version of any discrete object that counts c…
Finite generating functions for the sum of digits sequence
C. Vignat, T. Wakhare
We derive some new finite sums involving the sequence the sum of digits of the expansion of in base These functions allow us to generalize some clas…
Woon's tree and sums over compositions
C. Vignat, T. Wakhare
This article studies sums over all compositions of an integer. We derive a generating function for this quantity, and apply it to several special functions, including various gener…