We obtain an explicit formula for the linearization coefficient of the product of two associated q -ultraspherical polynomials in terms of a multiple of a balanced , terminating very - well - poised 10 蠁 9 series. We also discuss the nonnegativity properties of the coefficients as well as ...
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The product of two associated Legendre functions can be represented by a finite series in associated Legendre functions with unique coefficients. In this study a method is proposed to compute the coefficients in this product-sum formula. The method is of recursive nature and is based on the strai...
By using properties of orthogonal polynomials, the solid spherical harmonics are expressed in Cartesian form, thus providing a general basis for transformation... A Mohanty,E Clementi - 《International Journal of Quantum Chemistry》 被引量: 125发表: 1991年 Dirac-Fock self-consistent field method for...
and Verma, A.: Product and addition formulas for the continuous q-ultraspherical polynomials, SIAM J. Math. Anal. 17 (1986), 1461–1474. Google Scholar Rideau, G. and Winternitz, P.: Representations of the quantum algebra suq(2) on a real two-dimensional sphere, J. Math. Phys. 34 ...
Product and addition formulas for the continuous q -ultraspherical polynomials Using Askey and Wilson's orthogonality relation and Rahman's product formula for Askey–Wilson polynomials a Gegenbauer-type product formula is obtained fo... M Rahman,A Verma - Society for Industrial and Applied Mathematic...
, respectively. for the systematics model, we used polynomials in time and chose the optimal polynomial order for each segment individually that minimized the bic. we used exotep to calculate the posterior distributions of the free parameters through a joint mcmc fit of all light-curve segments....
In Section 2, we give some properties of ultraspherical polynomials. In Section 3, we discuss an algorithm for solving the 2nth-order elliptic linear differential equations subject to homogeneous boundary conditions using ultraspherical-Galerkin method (UGM). In Section 4, we are concerned with ...
only few powers of that matrix are bounded and we establish a connection between properties of the weight function and boundedness. In particular, we examine in detail two weight functions: the Laguerre weight functionforandand the ultraspherical weight function,,, and establish their properties. Bo...
In particular, using explicit formulas of ultraspherical polynomials, we are able to stretch Theorem 1 further and establish the following. Theorem 5 Main Let M be a product of compact Lie groups and spheres of odd dimension, equipped with a rational metric, of dimension d and rank r. Then...