Related papers: q-derivatives of multivariable q-hypergeometric fu…
Polynomial sequence ${P_m}_{m\geq0}$ is $q$-logarithmically concave if $P_{m}^2-P_{m+1}P_{m-1}$ is a polynomial with nonnegative coefficients for any $m\geq{1}$. We introduce an analogue of this notion for formal power series whose…
In this article, first we give two formulae for the delta invariant of a complex curve singularity that can be embedded as a ${\mathbb Q}$-Cartier divisor in a normal surface singularity with rational homology sphere link. Next, we consider…
HYPERDIRE is a project devoted to the creation of a set of Mathematica based programs for the differential reduction of hypergeometric functions. The current version includes two parts: the first one, FdFunction, for manipulations with…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. The associated special functions are eigenfunctions of some shape invariant operators. These operators can…
Motivated by the general problem of extending the classical theory of holomorphic functions of a complex variable to the case of quater- nion functions, we give a notion of an H-derivative for functions of one quaternion variable. We show…
In the paper, the authors find some new integral inequalities of Hermite-Hadamard type for functions whose derivatives of the $n$-th order are $(\alpha,m)$-convex and deduce some known results. As applications of the newly-established…
The structure of counterterms in higher derivative quantum gravity is reexamined. Nontrivial dependence of charges on the gauge and parametrization is established. Explicit calculations of two-loop contributions are carried out with the…
We first retell in the K-theoretic context the heuristics of $S^1$-equivariant Floer theory on loop spaces which gives rise to $D_q$-module structures, and in the case of toric manifolds, vector bundles, or super-bundles to their explicit…
This paper presents a new connection between the generalized Marcum-Q function and the confluent hypergeometric function of two variables, phi3. This result is then applied to the closed-form characterization of the bivariate Nakagami-m…
Let $(M,\,g)$ be a Poincar$\acute{\text{e}}$-Einstein manifold with a smooth defining function. In this note, we prove that there are infinitely many asymptotically hyperbolic metrics with constant $Q$-curvature in the conformal class of an…
We show that the Heun confluent equation admits infinitely many solutions in terms of the confluent generalized hypergeometric functions. For each of these solutions a characteristic exponent of a regular singularity of the Heun confluent…
We introduce a one parameter deformation of Zwegers' multivariable $\mu$-function by applying iterations of the $q$-Borel summation method, which is also a multivariate analogue of the generalized $\mu$-function introduced by the authors.…
The slightly subtle notion of covariant Lie derivatives of \textit{bundle-valued} differential forms is crucial in many applications in physics, notably in the computation of conserved currents in gauge theories, and yet the literature on…
The q-Legendre polynomials can be treated as some special "functions in the quantum double cosets $U(1)\setminus SU_q(2)/U(1)$". They form a family (depending on a parameter $q$) of polynomials in one variable. We get their further…
In this paper, we use the generalized q-polynomials with double q-binomial coefficients and homogeneous q-operators [J. Difference Equ. Appl. 20 (2014), 837--851.] to construct q-difference equations with seven variables, which generalize…
The coadjoint representation of a connected algebraic group $Q$ with Lie algebra $\mathfrak q$ is a thrilling and fascinating object. Symmetric invariants of $\mathfrak q$ (= $\mathfrak q$-invariants in the symmetric algebra $S(\mathfrak…
This lecture consists of two sections. In section 1 we consider the simplest version of a q-deformed Heisenberg algebra as an example of a noncommutative structure. We first derive a calculus entirely based on the algebra and then formulate…
The purpose of this note is to provide an alternative proof of two transformation formulas contiguous to that of Kummer's second transformation for the confluent hypergeometric function ${}_1F_1$ using a differential equation approach.
In the present paper combinatorial identities involving q-dual sequences or polynomials with coefficients q-dual sequences are derived. Further, combinatorial identities for q-binomial coefficients(Gaussian coefficients), q-Stirling numbers…
The paper deals with singularities of nonconfluent hypergeometric functions in several variables. Typically such a function is a multi-valued analytic function with singularities along an algebraic hypersurface. We describe such…