In a preceding paper [Comput. Phys. Commun. 184 (1): 51–59, 2013], we revisited the problem of calculating Coulomb Green’s function and image potential near a planar diffuse interface within which the dielectric permittivity of the inhomogeneous medium changes continuously along one Cartesian direction in a transition layer between two dissimilar dielectric materials. In the present paper, we c...

In this work, we employed the Laplace transform of right-sided distributions in conjunction with power series method to obtain distributional solutions modified Bessel equation and its related equation, whose coefficients contain parameters ν γ. We demonstrated that can be expressed as finite linear combinations Dirac delta function derivatives, specific form depending on values

A two-parameter sequence of orthogonal polynomials {Pn(x;λ,t)}n≥0 with respect to the weight function xαe−λxρν(xt),α>−1,λ,t≥0,ρν(x)=2xν/2Kν(2x),x>0,ν≥0, where Kν(z) is modified Bessel function, investigated. The case λ=0 corresponds Prudnikov and t = 0 related Laguerre polynomials. special one-parameter {Pn(x;1−t,t)}n≥0,t∈[0,1] analysed as well.

Two representations of the Bessel zeta function are investigated. An incomplete representation is constructed using contour integration and an integral due to Hawkins fully evaluated (analytically continued) produce two infinite series. This new representation, at integer values argument, produces results that consistent with known (values, slope, pole structure). Not surprisingly, studied foun...