Related papers: Integral Property of Laplace Operator
We utilize a combination of integral transforms, including the Laplace transform, with some classical results in analytic number theory concerning the Riemann $\xi$-function, to obtain a new integral equation. We also provide a new proof of…
In Rindler space, we determine in terms of special functions the expression of the static, massive scalar or vector field generated by a point source. We find also an explicit integral expression of the induced electrostatic potential…
This manuscript introduces a generalization of the Mellin integral transform within the framework of weighted fractional calculus with respect to an increasing function. The proposed transform is much more suitable for working with…
In this paper, additional properties of the lower gamma functions and the error functions are introduced and proven. In particular, we prove interesting relations between the error functions and Laplace transform.
In this paper, Lagrangian formalisms of Classical Mechanics was deduced on Kaehlerian manifold being geometric model of a generalized Lagrange space.Then, it was given two applications of complex Euler-Lagrange equations on mechanics…
Currently, some approaches to the associated Legendre functions based on different factorization methods are known. However, they have not allowed identifying new properties that permit to improve our knowledge of any physical system. In…
We present a method derived from Laplace transform theory that enables the evaluation of fractional integrals. This method is adapted and extended in a variety of ways to demonstrate its utility in deriving alternative representations for…
Defining the generalized charge, potential, current and generalized fields as complex quantities where real and imaginary parts represent gravitation and electromagnetism respectively, corresponding field equation, equation of motion and…
Based on previous work we consturct an equation (Lagrange equation) and relate it with a system of generalized integrals and differential equations in such a way to provide useful evaluations and connections between them.
The influence of electric stochastic fields on the relativistic charged particles is investigated in the gauge invariant path integral formalism. Using the cumulant expansion one finds the exponential relaxation of the charge Green's…
An invertible field transformation is such that the old field variables correspond one-to-one to the new variables. As such, one may think that two systems that are related by an invertible transformation are physically equivalent. However,…
In this paper, a generalised integral called the Laplace integral is defined on unbounded intervals, and some of its properties, including necessary and sufficient condition for differentiating under the integral sign, are discussed. It is…
This article is devoted to derivation of the Laplace transforms of the derivatives with respect to parameters of certain special functions, namely, the Mittag-Leffler type, Wright and Le Roy type functions. These formulas show…
The paper proposes a general notion of interaction between attributes, which can be applied to many fields in decision making and data analysis. It generalizes the notion of interaction defined for criteria modelled by capacities, by…
We extend the theory of distributional kernel operators to a framework of generalized functions, in which they are replaced by integral kernel operators. Moreover, in contrast to the distributional case, we show that these generalized…
The functions studied in the paper are quaternion-valued functions of a quaternionic variable. It is show that the left slice regular functions and right slice regular functions are related by a particular involution. The relation between…
Conventional electric field integral equation based theory is susceptible to the spurious internal resonance problem when the characteristic modes of closed perfectly conducting objects are computed iteratively. In this paper, we present a…
We study existence, uniqueness and regularity of solutions for linear equations in infinitely many derivatives. We develop a natural framework based on Laplace transform as a correspondence between appropriate $L^p$ and Hardy spaces: this…
The issue of electric charges in interaction with partially reflective surfaces is addressed by means of field theoretic methods. It is proposed an enlarged Maxwell lagrangian, describing the electromagnetic field in the presence of a…
Recently, it was found that a new set of simple techniques allow one to conveniently express ordinary integrals through differentiation. These techniques add to the general toolbox for integration and integral transforms such as the Fourier…