Our aim is to define modified Sz?sz type operators involving Charlier polynomials and obtain some approximation properties. We prove results on the order of convergence by using modulus smoothness Peetre?s K-functional. also establish Voronoskaja theorem for these operators. Moreover, we a Korovkin via q-statistical convergence.

Abstract About two dozens of exactly solvable Markov chains on one-dimensional finite and semi-infinite integer lattices are constructed in terms convolutions orthogonality measures the Krawtchouk, Hahn, Meixner, Charlier, q-Hahn, q-Meixner little q-Jacobi polynomials. By construction, stationary probability distributions, complete sets eigenvalues eigenvectors provided by polynomials measures. A...

Inspired by recent formul\ae\ of Dubrovin, Yang, and Zagier, we interpret the tau function enumerating stationary Gromov-Witten invariants $\mathbb{P}^1$ as an isomonodromic associated with a difference equation. As byproduct obtain analogue Kontsevich matrix model for this function. A connection Charlier ensemble is also considered.

In this paper classical solutions of the degenerate fifth Painlev\'e equation are classified, which include hierarchies algebraic and expressible in terms Bessel functions. Solutions known to third equation. Two applications these discussed, deriving exact complex sine-Gordon coefficients three-term recurrence relation associated with generalised Charlier polynomials.

Schwenzer, S. P.; Barnes, J. J.; Charlier, B. L.; Grady, M. M.; Hall, C.; Melwani Daswani, M.; Morse, A.; Olsson-Francis, K.; Patel, M.; Pearson, V.; Pillinger, J. M.; Preston, L. J.; Sheridan, S.; Sherlock, S. C.; Steer, E. D.; Summers, S.; Verchovsky, S.; Dove-Jay, A. S. ; Jewell, S. and Musilova, M. (2015). Containers, sensors and samples to understand desert weathering. In: 46th Lunar and P...

Schwenzer, S. P.; Barnes, J. J.; Charlier, B. L.; Grady, M. M.; Hall, C.; Melwani Daswani, M.; Morse, A.; Olsson-Francis, K.; Patel, M.; Pearson, V.; Pillinger, J. M.; Preston, L. J.; Sheridan, S.; Sherlock, S. C.; Steer, E. D.; Summers, S.; Verchovsky, S.; Dove-Jay, A. S. ; Jewell, S. and Musilova, M. (2015). Containers, sensors and samples to understand desert weathering. In: 46th Lunar and P...