Schützenberger groups and Chebyshev polynomials.
Selbstadjungierte Differentialoperatoren erster Ordnung in A2 (Co).
Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model.
Semi-orthogonality of a class of the gauss' hypergeometric polynomials
SO(2,1)-Invariant Double Integral Transforms and Formulas for the Whittaker Functions
MSC 2010: 33C15, 33C05, 33C45, 65R10, 20C40The paper contains some new formulas involving the Whittaker functions and arising as the values of some double integrals, which are invariant with respect to the representation of the group SO(2; 1).
Sobolev orthogonal polynomials: Interpolation and approximation.
Software for the algorithmic work with orthogonal polynomials and special functions.
Solution of option pricing equations using orthogonal polynomial expansion
We study both analytic and numerical solutions of option pricing equations using systems of orthogonal polynomials. Using a Galerkin-based method, we solve the parabolic partial differential equation for the Black-Scholes model using Hermite polynomials and for the Heston model using Hermite and Laguerre polynomials. We compare the obtained solutions to existing semi-closed pricing formulas. Special attention is paid to the solution of the Heston model at the boundary with vanishing volatility.
Some applications and numerical methods for orthogonal polynomials
Some bounding inequalities for the Jacobi and related functions.
Some computational formulas for -Nörlund numbers.
Some extensions of Bateman's product formulas for the Jacobi polynomials.
Some extremal properties of orthogonal polynomials.
Some formulas of L. Carlitz on Hermite polynomials.
Some generalisations of Chebyshev polynomials and their induced group structure over a finite field
Some generating functions for polynomials
Some generating functions involving the Stirling numbers of the second kind.
Some generating functions of Laguerre polynomials.
Some hypergeometric congruences
Some identities for Chebyshev polynomials.