We compute the master integrals for massless two-loop vertex graphs with three offshell legs. These master integrals are relevant for the QCD corrections to H → V V ∗ (where V = W , Z) and for two-loop studies of the triple gluon (and quark-gluon) vertex. We employ the differential equation technique to provide series expansions in ǫ for the various master integrals. The results are analytic an...

total or partial absence or excess of the sex chromosomes produces different karyotypes and phenotypical abnormalities. upon retrospective analysis of the results of 163444 cytogenetic tests that were performed during 28 years (1987-2015) in this center, different types of sex chromosomal aberrations and the clinical phenotypes are delineated in this article. moreover, the clinical course and t...

To study the effect of chemical and biological fertilizers on growth and essential oil content of lavender (Lavandula angustifolia Mill.), the present work was conducted in 2012-2013 at the experimental field of Alborz Research Station of the Research Institute of Forests and Rangelands, Karaj, Iran. The experiment was conducted in factorial in the form of a randomized complete block design wit...

in this paper an algorithm is presented for the regularization of singular integrals with any degrees of singularity, which may be employed in all three-dimensional problems analyzed by boundary elements. the integrals in boundary integrals equations are inherently singular. for example, one can mention the integrals confronted in potential problems to evaluate the flow or the gradient of the f...

In this report, we present two mathematical results which can be useful in a variety of settings. First, we present an analysis of Legendre polynomials triple product integral. Such integrals arise whenever two functions are multiplied, with both the operands and the result represented in the Legendre polynomial basis. We derive a recurrence relation to calculate these integrals analytically. W...

In this note, we are concerned with the asymptotic approximation of a class of double integrals which can be represented as an angular spectrum superposition. These double integrals typically appear in electromagnetic scattering problems. Based on the synthetic manipulation of the method of steepest descent path, approximate expressions of the double integrals are derived in terms of the leadin...