Region of convergence of derivative of Z transform

2016 ◽  
Vol 52 (8) ◽  
pp. 617-619 ◽  
Author(s):  
A.R. Forouzan
Keyword(s):  
Region Of Convergence

HOMOTOPY ANALYSIS METHOD TO SOLVE BOUSSINESQ EQUATIONS

2015 ◽  
Vol 10 (3) ◽  
pp. 2825-2833
Author(s):  
Achala Nargund ◽  
R Madhusudhan ◽  
S B Sathyanarayana
Keyword(s):  
Homotopy Analysis Method ◽  
Degrees Of Freedom ◽  
Initial Approximation ◽  
Boussinesq Equations ◽  
Convergent Series ◽  
Boussinesq System ◽  
Analysis Method ◽  
Analytical Technique ◽  
Homotopy Analysis ◽  
Region Of Convergence

In this paper, Homotopy analysis method is applied to the nonlinear coupleddifferential equations of classical Boussinesq system. We have applied Homotopy analysis method (HAM) for the application problems in [1, 2, 3, 4]. We have also plotted Domb-Sykes plot for the region of convergence. We have applied Pade for the HAM series to identify the singularity and reflect it in the graph. The HAM is a analytical technique which is used to solve non-linear problems to generate a convergent series. HAM gives complete freedom to choose the initial approximation of the solution, it is the auxiliary parameter h which gives us a convenient way to guarantee the convergence of homotopy series solution. It seems that moreartificial degrees of freedom implies larger possibility to gain better approximations by HAM.

scholarly journals The behaviour of the fourth type of Lauricella's hypergeometric series in n variables near the boundaries of its convergence region

1994 ◽  
Vol 57 (3) ◽  
pp. 281-294 ◽  
Author(s):  
Megumi Saigo ◽  
H. M. Srivastava
Keyword(s):  
Hypergeometric Function ◽  
Hypergeometric Functions ◽  
Hypergeometric Series ◽  
Convergence Region ◽  
Multiple Series ◽  
Fourth Type ◽  
Region Of Convergence

AbstractFor Lauricella's hypergeometric function F(n)D of n variables, we prove two formulas exhibiting its behaviour near the boundaries of the n-dimensional region of convergence of the multiple series defining it. Each of these results can be applied to deduce the corresponding properties of several simpler hypergeometric functions of one, two, and more variables.

A New Theory of Infinite Series and its Applications in Training Weight Function Neural Networks

2014 ◽  
Vol 513-517 ◽  
pp. 679-682
Author(s):  
Dai Yuan Zhang
Keyword(s):  
Neural Networks ◽  
Weight Function ◽  
Infinite Series ◽  
Feedforward Neural Networks ◽  
Function Expansion ◽  
Region Of Convergence ◽  
Better Than ◽  
Taylor’S Series

A new theory of infinite series is proposed in this paper, some new important theorems for function expansion and infinite series are also proposed. Unlike Taylors expansion, the expansion generated by a function is not the form of polynomials. In general, the performance of convergence is much better than that obtained by Taylor's Series. The new important theorems lay the foundation for the new theory of infinite series and applications. To describe the performance of the new results obtained in this paper, an example given in this paper shows that the region of convergence is much larger than that of Taylors series. The new infinite series can keep some important properties of original functions. Weight function neural networks are also used to training feedforward neural networks based on the new theory proposed in this paper.

A note on the region of convergence of the z-transform

2008 ◽  
Vol 88 (5) ◽  
pp. 1297-1298 ◽  
Author(s):  
C.S. Ramalingam
Keyword(s):  
Region Of Convergence

scholarly journals The Vibrations of a Particle about a Position of Equilibrium—Part III

1922 ◽  
Vol 41 ◽  
pp. 128-140
Author(s):  
Bevan B. Baker
Keyword(s):  
Dynamical System ◽  
Series Solution ◽  
Elliptic Functions ◽  
The Other ◽  
Real Solution ◽  
Present Part ◽  
Image Position ◽  
Region Of Convergence ◽  
Range Of Values ◽  
Made In

In the two parts of this investigation previously published it has been shown that the solution in terms of elliptic functions represents the motion of the particular dynamical system under consideration throughout the whole range of values of s and g for which a real solution exists, except for those values for which s = 2g and k = 1, but that, on the other hand, the series solution is convergent and represents the motion only so long asfor values of s and g for which the sign of this inequality is reversed the trigonometric series representing the solution are divergent. It is of importance to investigate what discontinuities, if any, of the system correspond to values of s and g which lie on the boundary of the region of convergence; the present part is concerned primarily with showing that under such circumstances no discontinuity of the system exists, thus confirming the suggestions made in Part I., § 12.

Sign in / Sign up

Export Citation Format

Share Document