In this paper, we define a group of solutions x(t) that are sine and cosine to the upper limit integration in non-elementary integral can be arbitrary. We will also equal amplitude. This is generalized amplitude function. using Abel’s methods, described by Armitage Eberlein. And finally, an exponential function whose exponent product complex number At least three groups functions special cases

Generalized log-sine functions Ls (k) j (θ) appear in higher order ε-expansion of different Feynman diagrams. We present an algorithm for numerical evaluation of these functions of real argument. This algorithm is implemented as C++ library with arbitrary-precision arithmetics for integer 0 ≤ k ≤ 9 and j ≥ 2. Some new relations and representations for the generalized log-sine functions are give...

In this paper, we investigate local and nonlocal reductions of a discrete negative order Ablowitz–Kaup–Newell–Segur equation. By the bilinearization reduction method, construct exact solutions in double Casoratian form to reduced sine-Gordon equations. Then, semidiscrete equations their are obtained through continuum limits. The dynamics soliton analyzed illustrated by asymptotic analysis. rese...

Abstract Motivated by the recent studies and developments of integral transforms with various special matrix functions, including orthogonal polynomials as kernels, in this article we derive formulas for Fourier cosine sine functions involving generalized Bessel polynomials. With help these several results are obtained, which extensions corresponding standard cases. The given here general chara...

We developed a CALL (computer-aided language learning) system for teaching the pronunciation of Japanese long vowels, the mora nasal and mora obstruents to nonnative speakers of Japanese. Long vowels and short vowels are spectrally almost identical but their phone durations differ significantly. Similar conditions exist between mora nasals and non-mora nasals, and between mora and non-mora obst...

Darboux transformation is constructed for superfields of the super sine-Gordon equation and the superfields of the associated linear problem. The Darboux transformation is shown to be related to the super Bäcklund transformation and is further used to obtain N super soliton solutions. PACS: 02.30.Ik PACS: 12.60.Jv mohsin [email protected] On study leave from PRD (PINSTECH) Islamabad, Pakistan mhassa...