A Note on Summabilityof Multiple Laguerre
نویسنده
چکیده
A simple structure of the multiple Laguerre polynomial expansions is used to study the Cess aro summability above the critical index for the convolution type Laguerre expansions. The multiple Laguerre polynomial expansion of an`1-radial function f 0 (jxj) is shown to be an`1-radial function that coincides with the Laguerre polynomial expansion of f 0 , which allows us to settle the problem of summability below the critical index for thè 1-radial functions.
منابع مشابه
A Note on Summability of Multiple Laguerre Expansions
A simple structure of the multiple Laguerre polynomial expansions is used to study the Cesàro summability above the critical index for the convolution type Laguerre expansions. The multiple Laguerre polynomial expansion of an `1-radial function f0(|x|) is shown to be an `1-radial function that coincides with the Laguerre polynomial expansion of f0, which allows us to settle the problem of summa...
متن کاملA Laguerre Polynomial Orthogonality and the Hydrogen Atom
The radial part of the wave function of an electron in a Coulomb potential is the product of a Laguerre polynomial and an exponential with the variable scaled by a factor depending on the degree. This note presents an elementary proof of the orthogonality of wave functions with differing energy levels. It is also shown that this is the only other natural orthogonality for Laguerre polynomials. ...
متن کاملControlling Nonlinear Processes, using Laguerre Functions Based Adaptive Model Predictive Control (AMPC) Algorithm
Laguerre function has many advantages such as good approximation capability for different systems, low computational complexity and the facility of on-line parameter identification. Therefore, it is widely adopted for complex industrial process control. In this work, Laguerre function based adaptive model predictive control algorithm (AMPC) was implemented to control continuous stirred tank rea...
متن کاملAn Extension of Bilateral Generating Functions of the Biorthogonal Polynomials Suggestedby Laguerre Polynomials
In this note, we have obtained a novel extension of a bilateral generating relationsinvolvingbiorthogonal polynomials ; from the existence of quasi-bilinear generating relation by group theoretic method. As particular cases, we obtain the corresponding results on generalised Laguerre polynomials.
متن کاملNotes on the BENCHOP implementations for the Fourier Gauss Laguerre FGL method
This text describes the Fourier pricing methods in general and the Fourier Gauss Laguerre FGL method and its implementation used the BENCHOP-project.
متن کامل