We conduct research in mathematics and computer science related to orthogonal polynomials and special functions. In the mathematics area, we investigate properties of the special functions of applied mathematics, especially series representations, definite integrals, and/or q-analogs of such expressions. In addition, we develop infinite series and definite integral expansions of fundamental solutions for linear elliptic partial differential equations on Riemannian manifolds of constant curvature (and/or their generalizations, the rank on symmetric spaces). Research in computer science includes the development of the software infrastructure to support the NIST online Digital Repository of Mathematical Formulae.

 

References

Cohl HS: Symmetry, Integrability and Geometry: Methods and Applications 9: 042, 2013

Cohl H, et al: Digital Repository of Mathematical Formulae, in Intelligent Computer Mathematics, Lecture Notes in Artificial Intelligence 8543. Springer, Edited by Watt SM, et al: 2014, 419422

 

Keywords:

Special functions; Orthogonal polynomials; Elliptic partial differential equations; Riemannian manifolds; Series expansions; Definite Integrals; Fundamental solutions; Mathematical knowledge management;

Citizenship:  Open to U.S. citizens

Level:  Open to Postdoctoral applicants