We obtain a closed form of generating functions of RNA substructure using hermitian matrix model with the Chebyshev polynomial of the second kind, which turns out to be the hypergeometric function. To match the experimental findings of the statistical behavior, we regard the substructure as a grand canonical ensemble and find its fugacity value. We also suggest a hierarchical picture based on t...

The main purpose of this article is to present an approximation method of for singular integrodifferential equations with Cauchy kernel in the most general form under the mixed conditions in terms of the second kind Chebyshev polynomials. This method transforms mixed singular integro-differential equations with Cauchy kernel and the given conditions into matrix equation and using the zeroes of ...

In this paper, we introduce the class of $(\beta,\gamma)$-Chebyshev functions and corresponding points, which can be seen as a family {\it generalized} Chebyshev polynomials points. For functions, prove that they are orthogonal in certain subintervals $[-1,1]$ with respect to weighted arc-cosine measure. particular investigate cases where become polynomials, deriving new results concerning clas...

For the Hahn and Krawtchouk polynomials orthogonal on the set {0, . . . , N} new identities for the sum of squares are derived which generalize the trigonometric identity for the Chebyshev polynomials of the first and second kind. These results are applied in order to obtain conditions (on the degree of the polynomials) such that the polynomials are bounded (on the interval [0, N ]) by their va...

In this paper, we consider a rational algorithm for modification of a positive measure by quadratic factor, dσ̂ (t) = (t − z)2 dσ(t), where it is allowed z to be in supp(dσ).Also, we present an application of modified algorithm to the measures dσ̂ (t) = T 2 2 (t) dσ(t) and dσ ′(t) = t2T 2 2 (t) dσ(t), where T2(t) = t2 − 1 2 is the second degree monic Chebyshev polynomial of the first kind and dσ(...

A spectral collocation method based on rational interpolants and adaptive grid points is presented. The rational interpolants approximate analytic functions with exponential accuracy by using prescribed barycentric weights and transformed Chebyshev points. The locations of the grid points are adapted to singularities of the underlying solution, and the locations of these singularities are appro...