New Karhunen-Loève expansions based on Hahn polynomials with application to a Sobolev test for uniformity on Johnson graphs by Pycke, Jean-Renaud

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Protecting Medical Images Using a Zero-Watermarking Approach Based on Fractional Racah Moments by Karim El-Khanchouli, Hanaa Mansouri, Nawal El Ghouate, Hicham Karmouni, Nour-Eddine Joudar, Mhamed Sayyouri, S. S. Askar, Mohamed Abouhawwash

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Fractional-order boundary value problems solutions using advanced numerical technique by Asmat Batool, Imran Talib, Muhammad Bilal Riaz

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Harmonic analysis on the quantized Riemann sphere by Jaak Peetre, Genkai Zhang

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Determinant inequalities for sieved ultraspherical polynomials by J. Bustoz, I. S. Pyung

“…Inequalities of this type have since been proved for both classical and nonclassical orthogonal polynomials. In this paper, we prove such an inequality for sieved orthogonal polynomials of the second kind.…”
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A note on the spectra of tridiagonal matrices by C. M. da Fonseca, J. Petronilho

“…Using orthogonal polynomials, we give a different approach to some recent results on tridiagonal matrices.…”
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Solving change of basis from Bernstein to Chebyshev polynomials by D.A. Wolfram

“…These results have applications in change of basis of orthogonal, and non-orthogonal polynomials.…”
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Tridiagonal Operators and Zeros of Polynomials in Two Variables by Chrysi G. Kokologiannaki, Eugenia N. Petropoulou, Dimitris Rizos

“…The polynomials in two variables are assumed to satisfy a five-term recurrence relation, similar to the three-term recurrence relation that the classical orthogonal polynomials satisfy.…”
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Analytical Solution for the Free Vibration Analysis of Delaminated Timoshenko Beams by Ramazan-Ali Jafari-Talookolaei, Maryam Abedi

“…The Legendre orthogonal polynomials are used as the beam eigenfunctions. …”
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Generalized Auto-Convolution Volterra Integral Equations: Numerical Treatments by Mahdi Namazi Nezamabadi, Saeed Pishbin

“…In this paper, we use the operational Tau method based on orthogonal polynomials to achieve a numerical solution of generalized autoconvolution Volterra integral equations. …”
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Solution of Some Types of Differential Equations: Operational Calculus and Inverse Differential Operators by K. Zhukovsky

“…We construct inverse differential operators and produce operational identities, involving inverse derivatives and families of generalised orthogonal polynomials, such as Hermite and Laguerre polynomial families. …”
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Hankel determinants and Jacobi continued fractions for $q$-Euler numbers by Chern, Shane, Jiu, Lin

“…It is shown that the associated orthogonal polynomials for $q$-Euler numbers are given by a specialization of the big $q$-Jacobi polynomials, thereby leading to their corresponding Jacobi continued fraction expressions, which eventually serve as a key to our determinant evaluations.…”
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On the Effect of Functionally Graded Materials on Resonances of Rotating Beams by Arnaldo J. Mazzei Jr.

“…An assumed mode approach is utilized, with the modes taken to be beam characteristic orthogonal polynomials. Results are obtained via Rayleigh-Ritz method and are compared for both the homogeneous and non-homogeneous cases. …”
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On the Effect of Functionally Graded Materials on Resonances of Rotating Beams by Arnaldo J. Mazzei Jr.

“…An assumed mode approach is utilized, with the modes taken to be beam characteristic orthogonal polynomials. Results are obtained via Rayleigh-Ritz method and are compared for both the homogeneous and non-homogeneous cases. …”
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Numerical and Experimental Approach for Identifying Elastic Parameters in Sandwich Plates by Sergio Ferreira Bastos, Lavinia Borges, Fernando A. Rochinha

“…The numerical method to calculate the natural frequencies involves the formulation of Rayleigh-Ritz using a series of characteristic orthogonal polynomials to properly model the free edge boundary conditions. …”
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(1,1)-Coherent Pairs on the Unit Circle by Luis Garza, Francisco Marcellán, Natalia C. Pinzón-Cortés

“…A pair (𝒰,𝒱) of Hermitian regular linear functionals on the unit circle is said to be a (1,1)-coherent pair if their corresponding sequences of monic orthogonal polynomials {ϕn(x)}n≥0 and {ψn(x)}n≥0 satisfy ϕn[1](z)+anϕn-1[1](z)=ψn(z)+bnψn-1(z), an≠0, n≥1, where ϕn[1](z)=ϕn+1′(z)/(n+1). …”
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A Semianalytic Method for Vibration Analysis of a Sandwich FGP Doubly Curved Shell with Arbitrary Boundary Conditions by Zhongyu Zhang, Jiayang Gu, Jianjun Ding, Yanwu Tao

“…For each segment, the displacement functions are selected as the Jacobi orthogonal polynomials and trigonometric series. The boundary conditions of the structure are obtained by the boundary spring simulation technique. …”
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Pell’s equation, sum-of-squares and equilibrium measures on a compact set by Lasserre, Jean B.

“…Interestingly, this view point connects orthogonal polynomials, Christoffel functions and equilibrium measures on one side, with sum-of-squares, convex optimization and certificates of positivity in real algebraic geometry on another side.…”
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Extensions of Riordan Arrays and Their Applications by Paul Barry

“…The Riordan group of Riordan arrays was first described in 1991, and since then, it has provided useful tools for the study of areas such as combinatorial identities, polynomial sequences (including families of orthogonal polynomials), lattice path enumeration, and linear recurrences. …”
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New Operational Matrix via Genocchi Polynomials for Solving Fredholm-Volterra Fractional Integro-Differential Equations by Jian Rong Loh, Chang Phang, Abdulnasir Isah

“…It is known that Genocchi polynomials have some advantages over classical orthogonal polynomials in approximating function, such as lesser terms and smaller coefficients of individual terms. …”
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