相关论文: Determination of the algebraic relations among spe…

Motivated by the substantial development of the special functions, we contribute to establish some rigorous results on the general series identities with bounded sequences and hypergeometric functions with different arguments, which are…

We introduce alternating multizeta values in positive characteristic which are generalizations of Thakur multizeta values. We establish their fundamental properties including non-vanishing, sum-shuffle relations, period interpretation and…

In this paper, we investigate new relationships for bilateral series related to two-parameter mock theta functions, which lead to many identities concerning the bilateral mock theta functions. In addition, interesting relations between the…

We prove or conjecture several relations between the multizeta values for positive genus function fields of class number one, focusing on the zeta-like values, namely those whose ratio with the zeta value of the same weight is rational (or…

In this paper we present several new classes of logarithmically completely monotonic functions. Our functions have in common that they are defined in terms of the $q-$gamma and $q-$digamma functions. As an applications of this results, some…

In our preceding article, we defined a generalized lambda function and showed that the genaralized lambda function and the modular invariant function generate the modular function field with respect to a principal congruence subgroup. In…

We develop an analogue of universal algebra in which generating symbols are interpreted as relations. We prove a variety theorem for these relational algebraic theories, in which we find that their categories of models are precisely the…

We consider the $m$-dimensional modified Helmholtz equation and establish two relations between its solutions in a bounded domain and harmonic functions. Both relations essentially rely on properties of the Newtonian potential. Some other…

We explore a number of functional properties of the $q$-gamma function and a class of its quotients; including the $q$-beta function. We obtain formulas for all higher logarithmic derivatives of these quotients and give precise conditions…

For each field k, we define an abelian category of rationally decomposed mixed motives with integer coefficients. When k is finite, we show that the category is Tannakian, and we prove formulas relating the behaviour of zeta functions near…

Let $g$ be a finite-dimensional simple Lie algebra over the complex number field. We classify the homomorphisms between $g$-modules induced from one-dimensional modules of maximal parabolic subalgebras.

We have derived some new results for the Mellin transform formulas, as well as for the Gauss hypergeometric function. Also, we have found the connection between the Legendre functions of the second kind. Some of the results obtained we used…

The first-order formulation of the principal sigma model with a Lie group target space is performed. By using the dualisation of the algebra and the field content of the theory the field equations which are solely written in terms of the…

We extend the classical links between valuations and orderings on fields to Tignol-Wadsworth gauges and positive cones on finite-dimensional simple algebras with involution. We also study the compatibility of gauges and positive cones, and…

In this survey, we outline the role of G-functions in arithmetic geometry, notably their link with Picard-Fuchs differential equations and periods. We explain how polynomial relations between special values of G-functions arising from a…

We prove new explicit asymptotic formulae between (geometric) eigenvalues in max-algebra and classical distinguished eigenvalues of nonnegative matrices, which are useful tools for transferring results between both settings. We establish…

Generating functions and functional equations of Dickson polynomials of the first and second kind are derived and continued analytically. These formulae are expressed in terms of the incomplete gamma function over complex variables of the…

The Digamma and Polygamma functions are important tools in mathematical physics, not only for its many properties but also for the applications in statistical mechanics and stellar evolution. In many textbooks is found its develop almost by…

We exhibit an explicit formula for the cardinality of solutions to a class of quadratic matrix equations over finite fields. We prove that the orbits of these solutions under the natural conjugation action of the general linear groups can…

Given an algebraic differential equation of order greater than one, it is shown that if there is any nontrivial algebraic relation amongst any number of distinct nonalgebraic solutions, along with their derivatives, then there is already…