Results 1 - 10 of 2288
Results 1 - 10 of 2288. Search took: 0.023 seconds
|Sort by: date | relevance|
[en] The Mahler measure for the n-variable polynomial k + ∑(xj + 1/xj) is reduced to a single integral of the n-th power of the modified Bessel function I0. Several special cases are examined in detail. This article is part of ‘Lattice models and integrability’, a special issue of Journal of Physics A: Mathematical and Theoretical in honour of F Y Wu's 80th birthday. (paper)
[en] In the present article, we wish to discuss q-analogues of Laplace-type integrals on diverse types of q-special functions involving Fox’s -functions. Some of the discussed functions are the q-Bessel functions of the first kind, the q-Bessel functions of the second kind, the q-Bessel functions of the third kind, and the q-Struve functions as well. Also, we obtain some associated results related to q-analogues of the Laplace-type integral on hyperbolic sine (cosine) functions and some others of exponential order type as an application to the given theory.
[en] In this paper the authors presents a simple Quasi-Fractional Approximation for Bessel Functions Jν(x), (- 1 ≤ ν < 0.5). This has been obtained by extending a method published which uses simultaneously power series and asymptotic expansions. Both functions, exact and approximated, coincide in at least two digits for positive x, and ν between - 1 and 0,4
[en] In this paper we consider the Hankel determinant defined for the coefficients of a function f which belongs to the class of univalent functions or to its subclasses: of starlike functions, of convex functions and of functions whose derivative has a positive real part. Bounds of for these classes are found; the bound for is sharp. Moreover, the sharp results for starlike functions and convex functions for which are obtained. It is also proved that is greater than 1.
[en] In the model of the inflaton nonminimal coupling to the Gauss–Bonnet term, we discuss the constant-roll inflation with constant ϵ, constant ϵ and constant η, respectively, with the additional assumption that δ is a constant. Using the Bessel function approximation, we get the analytical expressions for the scalar and tensor power spectrum and derive the scalar spectral index n and the tensor to scalar ratio r to the first order of ϵ. By using the Planck 2018 observations constraint on n and r, we obtain some feasible parameter space and show the result on the n−r region. The scalar potential is also reconstructed in some special cases.
[en] We integrate three-loop sunrise-type vacuum diagrams in dimensions with four different masses using configuration space techniques. The finite parts of our results are in numerical agreement with corresponding three-loop calculations in momentum space. Using some of the closed form results of the momentum space calculation we arrive at new integral identities involving truncated integrals of products of Bessel functions. For the non-degenerate finite two-loop sunrise-type vacuum diagram in dimensions we make use of the known closed form p-space result to express the moment of a product of three Bessel functions in terms of a sum of Clausen polylogarithms. Using results for the nondegenerate two-loop sunrise diagram from the literature in dimensions we obtain a Bessel function integral identity in terms of elliptic functions.
[en] Many algebraic equations satisfied by the zeros of the classical polynomials and of the Bessel functions are reported. Some of them are collected from recent papers; several of them are new; most of them display remarkable diophantine features. Certain matrices constructed with arbitrary numbers rather than the zeros of special functions, but displaying analogous diophantine properties, are also exhibited. (author)
[en] Applications of a simple approximation of Bessel functions of integer order, in terms of trigonometric functions, are discussed for several examples from electromagnetism and optics. The method may be applied in the intermediate regime, bridging the 'small values regime' and the 'asymptotic' one, and covering, in this way, an area of great physical interest. The examples that illustrate our approach are accessible to the undergraduate student