Related papers: A Short Note on Integral Transformations and Conve…
We introduce a novel, systematic method for the complete symbolic reduction of multi-loop Feynman integrals, leveraging the power of generating functions. The differential equations governing these generating functions naturally yield…
In this paper we have chosen to work with two different approaches to solving the inverse problem of the calculus of variation. The first approach is based on an integral representation of the Lagrangian function that uses the first…
A Generalised Hadamard Transform for multi-phase or multilevel signals is introduced, which includes the Fourier, Generalised, Discrete Fourier, Walsh-Hadamard and Reverse Jacket Transforms. The jacket construction is formalised and shown…
A recent generalization of the Central Limit Theorem consistent with nonextensive statistical mechanics has been recently achieved through a generalized Fourier transform, noted $q$-Fourier transform. A representation formula for the…
A class of Laplace transforms is examined to show that particular cases of this class are associated with production-destruction and reaction-diffusion problems in physics, study of differences of independently distributed random variables…
Recently the construction of various integral transforms for slice monogenic functions has gained a lot of attention. In line with these developments, the article at hand introduces the slice Fourier transform. In the first part, the kernel…
In this paper, we obtain analytical solutions of Laplace transform based some generalized class of the hyperbolic integrals in terms of hypergeometric functions ${}_3F_2 (\pm1)$, ${}_4F_3 (\pm1)$, ${}_5F_4(\pm1)$, ${}_6F_5(\pm1)$,…
The paper presents a new formula for the fractional integration, which generalizes the Riemann-Liouville and Hadamard fractional integrals into a single form, which when a parameter fixed at different values, produces the above integrals as…
In this paper, we extend the iterative expression for the generalized spherical functions associated to the root systems of type $A$ previously obtained beyond regular elements. We also provide the corresponding expression in the flat case.…
The double exponential formula was introduced for calculating definite integrals with singular point oscillation functions and Fourier-integrals. The double exponential transformation is not only useful for numerical computations but it is…
We show that the multiplication operator associated to a fractional power of a Gamma random variable, with parameter q>0, maps the convex cone of the 1-invariant functions for a self-similar semigroup into the convex cone of the q-invariant…
We investigate and solve a special class of integrals involving associated Legendre functions, which can be regarded as generalized Mehler-Fock transformations. Some of the integrals appear naturally when dealing with the heat or resolvent…
Our purpose in this present paper is to investigate generalized integration formulas containing the extended generalized hypergeometric function and obtained results are expressed in terms of extended hypergeometric function. Certain…
In this paper, we resort to the Laplace transform method in order to show its efficiency when approaching some types of fractional differential equations. In particular, we present some applications of such methods when applied to possible…
This is a compendium of generating functions involving single, double sums and definite integrals. These generating functions also involve special functions in both the summand function and closed form solution.
This paper introduces a unified theoretical perspective that views deep generative models as probability transformation functions. Despite the apparent differences in architecture and training methodologies among various types of generative…
We describe here an experimental method that permits to compute a good candidate for the closed form of a generating function if we know the first few terms of a series. The method is based on integer relations algorithms and uses either…
We apply a recently proposed approximation method to the evaluation of non-Gaussian integral and anharmonic oscillator. The method makes use of the truncated perturbation series by recasting it via the modified Laplace integral…
This paper establishes a real integral representation of the reciprocal $\Gamma$ function in terms of a regularized hypersingular integral. The equivalence with the usual complex representation is demonstrated. A regularized complex…
This paper presents a somewhat exhaustive study on the conformable fractional Gauss hypergeometric function (CFGHF). We start by solving the conformable fractional Gauss hypergeometric equation (CFGHE) about the fractional regular singular…