Hermite–Van Vleck polynomials
ثبت نشده
چکیده
We are interested in the special Heun equation, " special " means that all exponent differences are odd multiples of 1/2. Heun means 4 regular singularities.
منابع مشابه
Interlacing and asymptotic properties of Stieltjes polynomials
Polynomial solutions to the generalized Lamé equation, the Stieltjes polynomials, and the associated Van Vleck polynomials have been studied since the 1830’s, beginning with Lamé in his studies of the Laplace equation on an ellipsoid, and in an ever widening variety of applications since. In this paper we show how the zeros of Stieltjes polynomials are distributed and present two new interlacin...
متن کاملOperational matrices with respect to Hermite polynomials and their applications in solving linear differential equations with variable coefficients
In this paper, a new and efficient approach is applied for numerical approximation of the linear differential equations with variable coeffcients based on operational matrices with respect to Hermite polynomials. Explicit formulae which express the Hermite expansion coeffcients for the moments of derivatives of any differentiable function in terms of the original expansion coefficients of the f...
متن کاملOn Multiple Appell Polynomials
In this paper, we first define the multiple Appell polynomials and find several equivalent conditions for this class of polynomials. Then we give a characterization theorem that if multiple Appell polynomials are also multiple orthogonal, then they are the multiple Hermite polynomials.
متن کاملBernstein's polynomials for convex functions and related results
In this paper we establish several polynomials similar to Bernstein's polynomials and several refinements of Hermite-Hadamard inequality for convex functions.
متن کاملStrong asymptotics for relativistic Hermite polynomials
Strong asymptotic results for relativistic Hermite polynomials H n (z) are established as n, N →∞, thereby supplementing recent results on weak asymptotics for these polynomials. Depending on growth properties of the ratio N/n for the rescaled polynomials H n (cnz) (cn being suitable positive numbers, n, N →∞), formulae of Plancherel-Rotach type are derived on the oscillatory interval, in the c...
متن کامل