Related papers: Deformation Expression for Elements of Algebras (V…

We define and study analogues of exponentials for functions on noncommutative two-tori that depend on a choice of a complex structure. The major difference with the commutative case is that our noncommutative exponentials can be defined…

For a slice--regular quaternionic function $f,$ the classical exponential function $\exp f$ is not slice--regular in general. An alternative definition of exponential function, the $*$-exponential $\exp_*$, was given: if $f$ is a…

We define a noncommutative differential calculus constructed from the inner derivation, then several relevant examples are showed. It is of interest to note that for certain $C^*$-algebra, this calculus is closely related to the classical…

We develop the notion of deformations using a valuation ring as ring of coefficients. This permits to consider in particular the classical Gerstenhaber deformations of associative or Lie algebras as infinitesimal deformations and to solve…

This article gives a brief introduction to $q$-special functions, i.e., $q$-analogues of the classical special functions. Here $q$ is a deformation parameter, usually $0<q<1$, where $q=1$ is the classical case. The main topics to be treated…

We present a modular function-based approach to explaining, for primes larger than 3, the exponents that appear in the prime decomposition of the order of the monster finite simple group.

Let~$X=\Po/\Gamma$ be an~$n$-punctured sphere, $n>3$. We introduce and study~$n-3$ deformation operators on the space of modular forms~$M_*(\Gamma)$ based on the classical theory of uniformizing differential equations and accessory…

We first show that hypergeometric functions appear naturally as spectral functions when applying pseudo-differential calculus to decipher heat kernel asymptotic in the situation where the symbol algebra is noncommutative. Such observation…

A new integral representation is derived using a definite integral given by Cauchy and used to evaluate a number of integrals containing the finite series of special functions.

We extend the well-known Shannon decomposition of Boolean functions to more general classes of functions. Such decompositions, which we call pivotal decompositions, express the fact that every unary section of a function only depends upon…

We introduce the fractal expansions, sequences of integers associated to a number. We show that these sequences characterize the O-sequences and encode some information on lex segment ideals. Moreover, we introduce a numerical functions…

We obtain integral representations of the $n$-th derivatives of the Bessel functions with respect to the order. The numerical evaluation of these expressions is very efficient using a double exponential integration strategy. Also, from the…

Purpose of writing this paper is to solve a transcendental function containing a product of a variable and its double exponential by a unique method of approximation. If the value of the said product is given, then its inverse function is…

We define and study multivariate exponential functions, symmetric with respect to the alternating group A_n, which is a subgroup of the permutation (symmetric) group S_n. These functions are connected with multivariate exponential…

A class of well-behaved *-representations of a q-deformed Heisenberg algebra is studied and classified.

In this note, we presented a new decomposition of elements of finite fields of even order and illustrated that it is an effective tool in evaluation of some specific exponential sums over finite fields, the explicit value of some…

The problem of representation of elements of weighted space of infinitely differentiable functions on real line by exponential series is considered.

The complex exponential function is a local homeomorphism and gives therefore rise to an 'etale groupoid and a C*-algebra. We determine this algebra, as well as the alge bra of the complex conjugate of the exponential function.

It is a common knowledge that the integer functions definable in simply typed lambda-calculus are exactly the extended polynomials. This is indeed the case when one interprets integers over the type (p->p)->p->p where p is a base type…

Differintegral methods, currently exploited in calculus, provide a fairly unexhausted source of tools to be applied to a wide class of problems involving the theory of special functions and not only. The use of integral transforms of Borel…