Results 61 to 70 of about 395 (173)

Functional reduction of one-loop Feynman integrals with arbitrary masses

Journal of High Energy Physics, 2022
A method of functional reduction for the dimensionally regularized one-loop Feynman integrals with massive propagators is described in detail. The method is based on a repeated application of the functional relations proposed by the author.
O. V. Tarasov
doaj   +1 more source

Study of (p, q)‐Symmetric Starlike Functions of Order η

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
In the field of geometric function theory, we use the (p, q)‐differential operator in the complex unit disk to describe a novel class Sp,q∗∗η of symmetrical starlike functions of order η. Several interesting properties of functions belonging to the class Sp,q∗∗η are examined, such as growth, distortion, and convolution characteristics.
Imran Khan, Rashid Murtaza, Adnan, Mohammad Khalid Nasrat, Ozgur Ege   +4 more
wiley   +1 more source

Product and Quotient of Independent Gauss Hypergeometric Variables

Ingeniería y Ciencia, 2011
In this article, we have derived the probability density functions of the productand the quotient of two independent random variables having Gauss hypergeometricdistribution.
Daya Krishna Nagar, Danilo Bedoya Valencia   +1 more
doaj  

Series Solution to a Fuchsian‐Type Differential Equation in Terms of Orthogonal Polynomials

Journal of Mathematics, Volume 2026, Issue 1, 2026.
In this paper, we study a thirteen‐parameter Fuchsian‐type second‐order linear differential equation that involves five regular singularities. By employing a tridiagonal representation technique, we formulate four cases under which the series solutions of the equation are obtained in terms of Jacobi polynomials.
Saiful Rahman Mondal, Pratap Narayan Pathak, Smritijit Sen   +2 more
wiley   +1 more source

Celestial conformal blocks of massless scalars and analytic continuation of the Appell function F 1

Journal of High Energy Physics
In celestial conformal field theory (CCFT), the 4d massless scalars are represented by 2d conformal operators with conformal dimensions h = h ¯ $$ \overline{h} $$ = (1 + iλ)/2.
Wei Fan
doaj   +1 more source

Some Connections between the Spherical and Parabolic Bases on the Cone Expressed in terms of the Macdonald Function

Abstract and Applied Analysis, 2014
Computing the matrix elements of the linear operator, which transforms the spherical basis of SO(3,1)-representation space into the hyperbolic basis, very recently, Shilin and Choi (2013) presented an integral formula involving the product of two ...
I. A. Shilin, Junesang Choi
doaj   +1 more source

Parametric Transformations between the Heun and Gauss Hypergeometric Functions

Funkcialaj Ekvacioj, 2013
The hypergeometric and Heun functions are classical special functions. Transformation formulas between them are commonly induced by pull-back transformations of their differential equations, with respect to some coverings P1-to-P1. This gives expressions of Heun functions in terms of better understood hypergeometric functions. This article presents the
Vidunas, R., Filipuk, G.
openaire   +4 more sources

Expansions of the Solutions of the General Heun Equation Governed by Two-Term Recurrence Relations for Coefficients

Advances in High Energy Physics, 2018
We examine the expansions of the solutions of the general Heun equation in terms of the Gauss hypergeometric functions. We present several expansions using functions, the forms of which differ from those applied before.
T. A. Ishkhanyan, T. A. Shahverdyan, A. M. Ishkhanyan   +2 more
doaj   +1 more source

On a problem for mixed type equation with partial riemann-liouville fractional derivative

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2016
The uniqueness and existence of solutions of a nonlocal problem proved for an equation of mixed type. This equation contains diffusion equation of fractional order.
Oleg A Repin, Anna V Tarasenko
doaj   +1 more source

A Comprehensive Framework for Statistical Inference in Measurement System Assessment Studies

Applied Stochastic Models in Business and Industry, Volume 41, Issue 6, November/December 2025.
ABSTRACT Measurement system analysis aims to quantify the variability in data attributable to the measurement system and evaluate its contribution to overall data variability. This paper conducts a rigorous theoretical investigation of the statistical methods used in such analyses, focusing on variance components and other critical parameters.
Banafsheh Lashkari, Shojaeddin Chenouri
wiley   +1 more source