In this paper we deal with differential equations of the form yy ' = P(x, y) where y ' = dy/dx and P(x, y) is a polynomial in the variables x and y of degree n in the variable y. We provide an upper bound for the number ...

An algorithmic approach for generating generalised Zernike polynomials by differential operators and connection matrices is proposed. This is done by introducing a new order of generalised Zernike polynomials such that it ...

In a recent paper (Martínez-Finkelshtein et al. in Proc Am Math Soc 147:2625–2640, 2019) some interesting results were obtained concerning complementary Romanovski–Routh polynomials, a class of orthogonal polynomials on ...

We consider properties and applications of a sequence of polynomials Known as complementary RomanovsKi-Routh polynomials (CRR polynomials for short). These polynomials, which follow from the RomanovsKi-Routh polynomials ...

We study bivariate orthogonal polynomials associated with Freud weight functions depending on real parameters. We analyse relations between the matrix coefficients of the three term relations for the orthonormal polynomials ...

Consider the linear second-order differential equation An(z) y+ B-n(z) y' + C(n)y = 0, where A(n)(z) = a(2), nz(2) + a(1,n)z + a(0), n with a(2), n = 0, a2 1, n - 4a2, na0, n = 0,. n. N or a2, n = 0, a1, n = 0,. n. N, Bn(z) ...

The problem of existence and uniqueness of polynomial solutions of the Lamé differential equation A(x)y″ + 2B(x)y′ + C(x)y = 0, where A(x),B(x) and C(x) are polynomials of degree p + 1,p and p - 1, is under discussion. We ...

In this note we extend the classical relation between the equilibrium configurations of unit movable point charges in a plane electrostatic field created by these charges together with some fixed point charges and the ...