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We give an exposition of unpublished fragments of Gauss where he discovered (using a work of Jacobi) a remarkable connection between Napier pentagons on the sphere and Poncelet pentagons on the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.
Periodic points and dynamic rays of exponential maps.
Permanence of moment estimates for p-products of convex bodies
It is shown that two inequalities concerning second and fourth moments of isotropic normalized convex bodies in ℝⁿ are permanent under forming p-products. These inequalities are connected with a concentration of mass property as well as with a central limit property. An essential tool are certain monotonicity properties of the Γ-function.
Permutable functions.
Permutable polynomials for several variables.
Pfaff's method. III: Comparison with the WZ method.
Pick functions related to entire functions having negative zeros.
Plane partitions IV: A conjecture of Mills-Robbins-Rumsey.
Plane waves, biregular functions and hypercomplex Fourier analysis
Pochhammer symbol with negative indices. A new rule for the method of brackets
The method of brackets is a method of integration based upon a small number of heuristic rules. Some of these have been made rigorous. An example of an integral involving the Bessel function is used to motivate a new evaluation rule.
Polinomios ortogonales asociados con problemas espectrales