21 research outputs found
A generalization of Clausen's identity
The paper aims to generalize Clausen's identity to the square of any Gauss
hypergeometric function. Accordingly, solutions of the related 3rd order linear
differential equation are found in terms of certain bivariate series that can
reduce to 3F2 series similar to those in Clausen's identity. The general
contiguous variation of Clausen's identity is found. The related Chaundy's
identity is generalized without any restriction on the parameters of Gauss
hypergeometric function. The special case of dihedral Gauss hypergeometric
functions is underscored
Some functional equations related to the characterizations of information measures and their stability
The main purpose of this paper is to investigate the stability problem of
some functional equations that appear in the characterization problem of
information measures.Comment: 36 pages. arXiv admin note: text overlap with arXiv:1307.0657,
arXiv:1307.0631, arXiv:1307.0664, arXiv:1307.065
Upper bounds for the many‐channel Marchenko transformation operator and its derivatives
peer reviewedWe specify the class of perturbative complex matrix potentials for which the corresponding many-channel Marchenko type transformation operators are bounded and integrable. Our reference matrix potential contains Coulomb interactions, different threshold energies, and centrifugal potentials with different angular momenta. Estimates for the transformation operator and its derivatives are obtained; they enable us to improve our recent results and are necessary for the establishment of a unique solution to the ''generalized Marchenko fundamental equation.'' From the existence of an integrable transformation operator, the analyticity of the Jost solution as a function of k1 is deduced in the upper-half of the physical k1 plane