Later, Laguerre function
approximation is also introduced into the time domain reduction and it has been proven that in this case there exists an equivalent relationship to moment matching methods in the frequency domain [14-17].
First, the derivative of a Laguerre function
with respect to first argument can be expressed with Laguerre functions
of the same and lower order; that is,
For comparison with the existing approximation method, we consider the modified generalized Laguerre function
Tau method introduced in the literature  such as
The novel contribution is the comparison of the performance and online computation time of variants of MPC including GPC, nominally stable (closed-loop paradigm, dual- mode) MPC and Laguerre function
based MPC and a PID controller in simulation for the trajectory control of a Quadrotor helicopter
Sarkar, "Transient wave propagation in a general dispersive media using the laguerre function
in a marching-on-in-degree (MOD) methodology," Progress In Electromagnetics Research, Vol.
[L.sub.j](st) is the Laguerre function
 of order j with a scaling factor s, and [f.sub.n](r) represents the RWG function.
Identification method for commercialized PI control using Laguerre function
. In SICE Annual Conference, 13-18 September, pp.
Parameters that appear in the solution but not the partial-differential equation take discrete variables, imposed by boundary conditions, as follows: radial quantum number k and azimuthal quantum number l appear in generalized Laguerre function
R(r) in exactly the same form as in spherical polar coordinates because, after the separation of variables, the ordinarydifferential equation that governs R(r) is exactly the same in both spherical polar and spheroconical coordinates.
The aim of this paper is to develop the mixed generalized Laguerre-Legendre pseudospectral method for non-isotropic heat transfer in an infinite strip, by using the Legendre interpolation in the direction of finite length, and the generalized Laguerre function
interpolation in the infinite long direction.
In this directly generated solution of the governing partial-differential equation, the exponential term containing distance r directly contains a minus sign, implying an exponential decay of [psi](r,[theta],[phi]) as r [right arrow] [infinity]; if a plus sign appeared in that direct solution, that formula might still be acceptable, provided that a polynomial factor in r, here expressed as an associated Laguerre function
, generally denoted [Lk.sup.2l+1](r), as a product with associated Legendre functions of the first kind , generally denoted [Pl.sup.m](cos [theta]), possesses an appropriate form .
Wang  studied the Fisher equation on a semi-infinite domain using the generalized Laguerre functions
. Wang and Jiao  considered the Fisher equation on unbounded domain using the generalized Hermite functions.
In particular, the polyBergman spaces are spaces of Wavelet transform which is related to Laguerre functions
, and the poly-Fock spaces are spaces of short-time Fourier transform which is related to Hermite functions.