The paper advances Odake and Sasaki’s idea to re-write eigenfunctions of rationally deformed Morse potentials in terms Wronskians Laguerre polynomials the reciprocal argument. It is shown that constructed quasi-rational seed solutions Schrödinger equation with potential are formed by generalized Bessel degree-independent indexes. As a new achievement we can point construction Darboux-Crum net i...

Singular perturbation problems have been studied by many mathematicians. Since the approximate solutions of these problems are as the sum of internal solution (boundary layer area) and external ones, the formation or non-formation of boundary layers should be specified. This paper, investigates this issue for a singular perturbation problem including a first order differential equation with gen...

We find sets of solutions to the generalized spheroidal wave equation (GSWE) or, equivalently, to the confluent Heun equation. Each set is constituted by three solutions, one given by a series of ascending powers of the independent variable, and the others by series of regular and irregular confluent hypergeometric functions. For a fixed set, the solutions converge over different regions of the...

If H denotes the classical Hilbert transform and Hu(x) = v(x), then the functions u(x) and v(x) are the values on the real axis of a pair of conjugate functions, harmonic in the upper half-plane. This note gives a generalization of the above concepts in which the Laplace equation Deltau = 0 is replaced by the Yukawa equation Deltau = mu(2)u and in which the Cauchy-Riemann equations have a corre...

Special functions such as hypergeometric, zeta, Bessel, Whittaker, Struve, Airy, Weber-Hermite and Mittag-Leffler are obtained a solution to complex differential equations in engineering, science technology. In this work, generalized Euler-type integrals involving four parameters function proposed. Some special cases of type that corresponding well-known results the literature also inferred.

The paper is concerned with the study of magneto-thermoelastic interactions in three dimensional thermoelastic medium under the purview of three-phase-lag model of generalized thermoelasticity. The medium under consideration is assumed to be homogeneous orthotropic medium. The fundamental equations of the three-dimensional problem of generalized thermoelasticity are obtained as a vector-matrix ...

This paper provides an exact approach for free transverse vibration analysis of a simply supported non-uniform Euler-Bernoulli beam with an arbitrary number of concentrated cracks. The equation of motion is normalized and written based on a set of dimensionless parameters. The general solution is obtained based on the Bessel functions. The differential equation is modified to include cracks. Th...

The present paper aims at the study and derivation of Saigo generalized fractional integral operator involving product of Hfunction of one variable and general class of polynomials. On account of the most general nature of the operator, H-function and general class of polynomials occurring in the main result, a large number of known and new results involving Rieman-Liouville, ErdélyiKober Fract...