Related papers: General One-loop Generating Function by IBP relati…

In this paper, we discuss how to apply GAP to do computations in modular representation theory. Of particular interest is the generating number of a group algebra, which measures the failure of the generating hypothesis in the stable module…

The aim of this paper is to study generating functions for the coefficients of the classical superoscillatory function associated with weak measurements. We also establish some new relations between the superoscillatory coefficients and…

In this paper it is shown how the generating functional for Green's functions in relativistic quantum field theory and in thermal field theory can be evaluated in terms of a standard quantum mechanical path integral. With this calculational…

The existence of a finite basis of algebraically independent one-loop integrals has underpinned important developments in the computation of one-loop amplitudes in field theories and gauge theories in particular. We give an explicit…

A procedure is described that makes use of the generating function of characters to obtain a new generating function $H$ giving the multiplicities of each weight in all the representations of a simple Lie algebra. The way to extract from…

There is an increasing interest in scaling tensor network methods through belief propagation (BP), as well as increasing the accuracy of BP through tensor network methods. We develop a unification framework that takes an arbitrary graphical…

We present a new method for the calculation of differential distributions directly in Mellin space without recourse to the usual momentum-fraction (or z-) space. The method is completely general and can be applied to any process. It is…

We derive recursions for the probability distribution of random sums by computer algebra. Unlike the well-known Panjer-type recursions, they are of finite order and thus allow for computation in linear time. This efficiency is bought by the…

We show how to construct a complete set of lowering operators, whose successive application reduces an arbitrary Fenyman integral to a combination of master integrals. The construction builds systems of equations for generic integral…

Recent results by Andrews and Merca on the number of even parts in all partitions of n into distinct parts, a(n), were derived via generating functions. This paper extends these results to the number of parts divisible by k in all the…

For an odd prime p, we determine a minimal set of topological generators of the pro-p Iwahori subgroup of a split reductive group G over Z\_p. In the simple adjoint case and for any sufficiently large regular prime p, we also construct…

We define a modular function which is a generalization of the elliptic modular lambda function. We show this function and the modular invariant function generate the modular function field with respect to the principal congruence subgroup.…

Certain classical generating functions for elements of reflection groups can be expressed using fundamental invariants called exponents. We give new analogues of such generating functions that accommodate orbits of reflecting hyperplanes…

A new method for the reduction of one-loop tensor 5-point integrals to related 4-point integrals is proposed. In contrast to the usual Passarino-Veltman reduction and other methods used in the literature, this reduction avoids the…

This paper proposes a new volume function for calculation of the entropy of planar granular assemblies. This function is extracted from the antisymmetric part of a new geometric tensor and is rigorously additive when summed over grains. It…

In this paper, using geometric polynomials, we obtain a generating function of p-Bernoulli numbers. As a consequences this generating function, we derive closed formulas for the finite summation of Bernoulli and harmonic numbers involving…

The commutator calculus is one of the basic tools in group theory. However, its extension to the non-associative context, based on the usual definition of the lower central series of a loop, is not entirely satisfactory. Namely, the graded…

We propose a new method of calculation of generating functions of Chebyshev polynomials in several variables associated with root systems of simple Lie algebras. We obtain the generating functions of the polynomials in two variables…

Starting with two copies of the random energy model coupled with independent magnetic fields, the generating function for the connected correlator of the magnetization is exactly derived. Without use of the replica trick, it is shown that…

For the sl_2 Gaudin model (degenerated quantum integrable XXX spin chain) an exponential generating function of correlators is calculated explicitely. The calculation relies on the Gauss decomposition for the SL_2 loop group. From the…