Orthogonal polynomials associated with root systems.
Orthogonal Polynomials for the Oscillatory-gegenbauer Weight
Orthogonal polynomials on the radial rays and an electrostatic interpretation of zeros.
Orthogonal polynomials on the semicircle
Orthogonal polynomials related to the oscillatory-chebyshev weight function
Orthogonal -polynomials related to perturbed linear form.
Orthogonality of Jacobi polynomials with general parameters.
Orthogonality relations for multivariate Krawtchouk polynomials.
Orthogonality within the families of -, -, and -functions of any compact semisimple Lie group.
Overpartition pairs
An overpartition pair is a combinatorial object associated with the -Gauss identity and the summation. In this paper, we prove identities for certain restricted overpartition pairs using Andrews’ theory of recurrences for well-poised basic hypergeometric series and the theory of Bailey chains.
Padé and Hermite-Padé approximation and orthogonality.
Padé-Type Approximants of Exp (-z) Whose Denominators Are (1+z/n)n.
Parameter augmentation for two formulas.
Partial Quasi-Bilateral Generating Function Involving some Special Functions
A group-theoretic method of obtaining more general class of generating functions from a given class of partial quasi-bilateral generating functions involving Hermite, Laguerre and Gegenbaur polynomials are discussed.
Partial sums of two quartic -series.
Particular solutions for a class of ODE related to the -exponential functions.
Partition statistics and -Bell numbers .
Partitions, q-Series and the Lusztig-Macdonald-Wall Conjectures.
Pentagramma mirificum and elliptic functions (Napier, Gauss, Poncelet, Jacobi, ...)
We give an exposition of unpublished fragments of Gauss where he discovered (using a work of Jacobi) a remarkable connection between Napier pentagons on the sphere and Poncelet pentagons on the plane. As a corollary we find a parametrization in elliptic functions of the classical dilogarithm five-term relation.
Periodic integrals and tautological systems
We study period integrals of CY hypersurfaces in a partial flag variety. We construct a regular holonomic system of differential equations which govern the period integrals. By means of representation theory, a set of generators of the system can be described explicitly. The results are also generalized to CY complete intersections. The construction of these new systems of differential equations has lead us to the notion of a tautological system.