Computation of the Entropy of Polynomials Orthogonal on an Interval
نویسندگان
چکیده
We give an effective method to compute the entropy for polynomials orthogonal on a segment of the real axis that uses as input data only the coefficients of the recurrence relation satisfied by these polynomials. This algorithm is based on a series expression for the mutual energy of two probability measures naturally connected with the polynomials. The particular case of Gegenbauer polynomials is analyzed in detail. These results are applied also to the computation of the entropy of spherical harmonics, important for the study of the entropic uncertainty relations as well as the spatial complexity of physical systems in central potentials.
منابع مشابه
Buckling and vibration analysis of angle -ply symmetric laminated composite plates with fully elastic boundaries
The main focus of this paper is on efficiency analysis of two kinds of approximating functions (characteristic orthogonal polynomials and characteristic beam functions) that have been applied in the Rayleigh-Ritz method to determine the non-dimensional buckling and frequency parameters of an angle ply symmetric laminated composite plate with fully elastic boundaries. It has been observed that o...
متن کاملSolving singular integral equations by using orthogonal polynomials
In this paper, a special technique is studied by using the orthogonal Chebyshev polynomials to get approximate solutions for singular and hyper-singular integral equations of the first kind. A singular integral equation is converted to a system of algebraic equations based on using special properties of Chebyshev series. The error bounds are also stated for the regular part of approximate solut...
متن کاملMathematical Modeling of Gas Adsorption Processes in Packed Bed: The Role of Numerical Methods on Computation Time
Rigorous mathematical modeling of adsorption processes in packed beds involves time-consuming computations which are considered as the fundamental weakness of such thorough mathematical models. Thus, reducing the computation time was a key factor in improving adsorption mathematical models. In order to achieve this goal, an attempt was made to know how much using different numerical methods inf...
متن کاملRecurrences and explicit formulae for the expansion and connection coefficients in series of the product of two classical discrete orthogonal polynomials
Suppose that for an arbitrary function $f(x,y)$ of two discrete variables, we have the formal expansions. [f(x,y)=sumlimits_{m,n=0}^{infty }a_{m,n},P_{m}(x)P_{n}(y),] $$ x^{m}P_{j}(x)=sumlimits_{n=0}^{2m}a_{m,,n}(j)P_{j+m-n}(x),$$ we find the coefficients $b_{i,j}^{(p,q,ell ,,r)}$ in the expansion $$ x^{ell }y^{r},nabla _{x}^{p}nabla _{y}^{q},f(x,y)=x^{ell }y^{r}f^{(p,q)}(x,y) =sumli...
متن کاملComputation on Zagreb Polynomial of Some Families of Dendrimers
In mathematical chemistry, a particular attention is given to degree-based graph invariant. The Zagrebpolynomial is one of the degree based polynomials considered in chemical graph theory. A dendrimer isan artificially manufactured or synthesized molecule built up from branched units called monomers. Inthis note, the first, second and third Zagreb poly...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM J. Scientific Computing
دوره 26 شماره
صفحات -
تاریخ انتشار 2004