The 15 Gauss contiguous relations for 2F1 hypergeometric series imply that any three 2F1 series whose corresponding parameters differ by integers are linearly related (over the field of rational functions in the parameters). We prove several properties of coefficients of these general contiguous relations, and use the results to propose effective ways to compute contiguous relations. We also di...

We consider the problem of generating the recursion coefficients of orthogonal polynomials for a given weight function. The weight function is assumed to be the weighted sum of weight functions, each supported on its own interval. Some of these intervals may coincide, overlap or are contiguous. We discuss three algorithms. Two of them are based on modified moments, whereas the other is based on...

Abstract 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 identit...

Over the last years two-photon excitation 4Pi-microscopy with an axial resolution of ~100 nm has been demonstrated in multiple biological applications [1-3]. The artefact-free presentation of the recorded structures has been possible because of the contiguous optical transfer function (OTF), which allows reliable image deconvolution. The use of two-photon excitation (2PE) has been critical to s...

The tree sequence based translation model allows the violation of syntactic boundaries in a rule to capture non-syntactic phrases, where a tree sequence is a contiguous sequence of subtrees. This paper goes further to present a translation model based on non-contiguous tree sequence alignment, where a non-contiguous tree sequence is a sequence of sub-trees and gaps. Compared with the contiguous...

The Haldane phase is the prototype of symmetry protected topological (SPT) phases spin chain systems. It can be by several symmetries having in common degeneracy entanglement spectrum. Here we explore depth this for spin-1 AKLT and bilinear-biquadratic Hamiltonians show emergence a bulk-edge correspondence that relates low energy properties Hamiltonian periodic physical an open chain. We find s...

The main objects of the investigation presented in this paper are branched-continued-fraction representations ratios contiguous hypergeometric series and type II multiple orthogonal polynomials on step-line with respect to linear functionals or measures whose moments products Pochhammer symbols. This is an interesting case study recently found connection between branched continued fractions tha...

Choosing the financial supply is one of the most important decisions for providing optimal structure that can be effective for firm value and stocks market of companies. Therefore, marketing as one of the abilities of the firm can be effective on firm function. The purpose of this research is studying the role of marketing intensity on the relation of financial leverage and firm function in Com...