Related papers: Applications of generalized trigonometric function…
A general formalism to solve nonlinear differential equations is given. Solutions are found and reduced to those of second order nonlinear differential equations in one variable. The approach is uniformized in the geometry and solves…
Asymptotic expansions for generalised trigonometric integrals are obtained in terms of elementary functions, which are valid for large values of the parameter $a$ and unbounded complex values of the argument. These follow from new…
We present numerical techniques based on generalized functions adapted to nonlinear calculations. They concern main numerical engineering problems ruled by-or issued from-nonlinear equations of continuum mechanics. The aim of this text is…
(Draft 3) A generalized differential operator on the real line is defined by means of a limiting process. These generalized derivatives include, as a special case, the classical derivative and current studies of fractional differential…
Present and future high-precision tests of the Standard Model and beyond for the fundamental constituents and interactions in Nature are demanding complex perturbative calculations involving multi-leg and multi-loop Feynman diagrams.…
In this paper, we use some standard numerical techniques to approximate the hypergeometric function $$ {}_2F_1[a,b;c;x]=1+\frac{ab}{c}x+\frac{a(a+1)b(b+1)}{c(c+1)}\frac{x^2}{2!}+\cdots $$ for a range of parameter triples $(a,b,c)$ on the…
Hypergeometric functions and their generalizations play an important r\^{o}les in diverse applications. Many authors have been established generalizations of hypergeometric functions by a number ways. In this paper, we aim at establishing…
The Gelfand-Yaglom formula relates functional determinants of the one-dimensional second order differential operators to the solutions of the corresponding initial value problem. In this work we generalise the Gelfand-Yaglom method by…
In this manuscript, we generalize F-calculus to apply it on fractal Tartan spaces. The generalized standard F-calculus is used to obtain the integral and derivative of the functions on the fractal Tartan with different dimensions. The…
This paper explores the calculus of dual-valued functions and investigates the gamma function, beta function and generalized hypergeometric functions by incorporating dual numbers as parameters and variables. We examine its fundamental…
Based on the generalized Boltzmann equation and the reverse function of the distribution function, we investigate the two-parameter generalized statistics and get an expression between the two parameters (k,r) and the physical quantities…
General theory of elliptic hypergeometric series and integrals is outlined. Main attention is paid to the examples obeying properties of the "classical" special functions. In particular, an elliptic analogue of the Gauss hypergeometric…
This text is addressed to mathematicians who are interested in generalized functions and unbounded operators on a Hilbert space. We expose in detail (in a "formal way" - as done by Heisenberg and Pauli - i.e. without mathematical…
We provide definitions of renormdynamic motion equations and some properties of renormdynamic functions with examples. Formal, longwave and shortwave solutions of the canonical equation for generalized (pseudo) analytic functions (GPF) are…
In this paper the double-sided Talor's approximations are used to obtain generalisations and improvements of some trigonometric inequalities.
We generate Gaussian radial function based higher order compact RBF-FD formulas for some differential operators. Analytical expressions for weights associated to first and second derivative formulas (up to order 10) and 2D-Laplacian…
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…
Generalized Functions play a central role in the understanding of differential equations containing singularities and nonlinearities. Introducing infinitesimals and infinities to deal with these obstructions leads to controversies…
In this note, we present two general classes of integral inequalities motivated by their applications to infinite dimensional systems. The inequalities possess general structures in terms of weight functions and lower quadratic bounds. Many…
In this article, we present a new two-dimensional generalization of the gamma function based on the product of the one-dimensional generalized beta function and the one-dimensional generalized gamma function. As will become clear later,…