Related papers: On the recursion formulas of Lauricella matrix fun…

We prove sum representations of Appell-Lauricella functions over a finite field using confluent hypergeometric functions over the finite field. As an application, we also prove transformation formulas, summation formulas and reduction…

We express explicitly the Heckman-Opdam hypergeometric function for the root system of type A with a certain degenerate parameter in terms of the Lauricella hypergeometric function.

Family of replica matrices, related to general ultrametric spaces, is introduced. These matrices generalize the known Parisi matrices. Some functionals of replica approach are computed.

We calculate the fractional Laplacian for functions of the form $u(x)=(1-|x|^2)_+^p$ and $v(x)=x_d u(x)$. As an application, we estimate the first eigenvalues of the fractional Laplacian in a ball.

We present a derivation of the dynamical r-matrices of the Calogero-Moser models using the Hamiltonian reduction procedure to get general formulae. We describe the dynamical r-matrices thus found for spin Calogero-Moser models and…

In this work, we define a more general family of polynomials in several variables satisfying a linear recurrence relation. Then we provide explicit formulas and determinantal expressions. Finally, we apply these results to recurrent…

We present a unified approach which gives completely elementary proofs of three weighted sum formulae for double zeta values. This approach also leads to new evaluations of sums relating to the harmonic numbers, the alternating double zeta…

The aim of this note is to give some factorization formulas for different versions of the Macdonald polynomials when the parameter t is specialized at roots of unity, generalizing those existing for Hall-Littlewood functions.

In this paper, we derive certain formulas giving the Laplace transforms of two generalized fractional integral operators introduced recently in [Fract. Calc. Appl. Anal. 20 (2) (2017), 422--446]. The main results provide generalizations to…

We derive, under a technical assumption, the first variation formula for the eigenvalues of the Laplacian on a closed manifold evolving by the Ricci flow and give some applications.

We consider non-linear generalizations of fractal interpolating functions applied to functions of one and two variables. The use of such interpolating functions in resizing images is illustrated.

For a rational matrix function R of one variable in general position, the matrix functions R(x)/R(y) and R(y)\R(x) of two variables are considered. For these matrix functions of two variables, representations which are analogous to the…

In the paper the author presents limit formulas for ratios of polygamma functions at their singularities.

Determinant formulas are presented for: a certain positive semidefinite, hermitian matrix; the loss value of multilinear regression; the multiple linear regression coefficient.

A procedure to obtain differentiation matrices is extended straightforwardly to yield new differentiation matrices useful to obtain derivatives of complex rational functions. Such matrices can be used to obtain numerical solutions of some…

This is a short review of some recent results obtained by the author. These results are related the problem of obtaining polynomial identities (computational formulas) for some matrix functions by means of the known polarization theorem,…

Following our earlier work, where doubly indexed and irreducible over Q two-variable Laguerre polynomials were introduced, we prove for such polynomials some recurrence formulas and obtain a generating function. In addition, we show how…

We compute the sum and the alternating sum of the reciprocals of triangular numbers using two standard methods from calculus: a telescoping series approach and a power series approach. We then extend these results to generalized…

In this short notes, we discuss monotonicity formulas under various rescaled versions of Ricci flow. The main result is Theorem \ref{theo rescaled}.

We prove general fomulas for the deviations of two overpartition ranks from the average. These formulas are in terms of Appell--Lerch series and sums of quotients of theta functions and can be used, among other things, to recover any of the…