Related papers: More Special Functions Trapped
In this article we analyze a generalized trapezoidal rule for initial value problems with piecewise smooth right hand side \(F:\R^n\to\R^n\). When applied to such a problem the classical trapezoidal rule suffers from a loss of accuracy if…
Interpolation of classes of differentiated functions given on a finite interval by trigonometric splines using the phantom node method is considered. This method consists in supplementing a given sequence of values of an approximate…
Studying Birkhoff sums of non-integrable functions involves the challenge of large observations depending on the sampled orbit, which prevents pointwise limit theorems. To address this issue, the largest observations are removed, this…
Generalized integral formulas involving the generalized Bessel-Maitland function are considered and it expressed in terms of generalized Wright hypergeometric functions. By assuming appropriate values of the parameters in the main results,…
Although Feynman integrals in general cannot be expressed as well-studied special functions, they can be calculated systematically and efficiently using the \texttt{AMFlow} method in combination with differential equations in the kinematic…
A number of new definite integrals involving Bessel functions are presented. These have been derived by finding new integral representations for the product of two Bessel functions of different order and argument in terms of the generalized…
Matrix functions with potential applications have a major role in science and engineering. One of the fundamental matrix functions, which is particularly important due to its connections with certain matrix differential equations and other…
In this article, we describe a new algorithm for the expansion of hypergeometric functions about half-integer parameters. The implementation of this algorithm for certain classes of hypergeometric functions in the already existing…
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…
We study a number of possible extensions of the Ramanujan master theorem, which is formulated here by using methods of Umbral nature. We discuss the implications of the procedure for the theory of special functions, like the derivation of…
In this paper, by using the residue theorem and asymptotic formulas of trigonometric and hyperbolic functions at the poles, we establish many relations involving two or more infinite series of trigonometric and hyperbolic trigonometric…
Dawson's integral and related functions in mathematical physics that include the complex error function (Faddeeva's integral), Fried-Conte (plasma dispersion) function, (Jackson) function, Fresnel function and Gordeyev's integral are…
In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are quasi-convex. Some applications to special means of real…
The Heckman-Opdam hypergeometric functions of type BC extend classical Jacobi functions in one variable and include the spherical functions of non-compact Grassmann manifolds over the real, complex or quaternionic numbers. There are various…
Using elementary methods, we define and derive a particular weighted average of the trapezoidal and composite trapezoidal rules and show that this approximation, as well as its composite, is straightforward in computation. This…
An analytical method is advanced for constructing interpolation formulae for complicated problems of statistical mechanics, in which just a few terms of asymptotic expansions are available. The method is based on the self-similar…
We describe some "unrestricted" algorithms which are useful for the computation of elementary and special functions when the precision required is not known in advance. Several general classes of algorithms are identified and illustrated by…
In this paper, some new inequalities of the Hermite-Hadamard type for functions whose modulus of the derivatives are convex and applications for special means are given. Finally, some error estimates for the trapezoidal formula are…
Investigation of the generalized trigonometric and hyperbolic functions containing two parameters has been a very active research area over the last decade. We believe, however, that their monotonicity and convexity properties with respect…
In this work we develop the Gaussian quadrature rule for weight functions involving fractional powers, exponentials and Bessel functions of the first kind. Besides the computation based on the use of the standard and the modified Chebyshev…