scholarly journals Computational Analysis of Generalized Zeta Functions by Using Difference Equations

2020 ◽  
Author(s):  
Asifa Tassaddiq
Keyword(s):  
Difference Equations ◽  
Taylor Series ◽  
Computational Analysis ◽  
Zeta Functions ◽  
Series Expansions ◽  
Graphical Representations ◽  
Computational Power ◽  
Numerical Computations ◽  
Taylor Series Expansions

In this article, author performs computational analysis for the generalized zeta functions by using computational software Mathematica. To achieve the purpose recently obtained difference equations are used. These difference equations have a computational power to compute these functions accurately while they can not be computed by using their known integral represenations. Several authors investigated such functions and their analytic properties, but no work has been reported to study the graphical representations and zeors of these functions. Author performs numerical computations to evaluate these functions for different values of the involved parameters. Taylor series expansions are also presented in this research.

scholarly journals A Shortcut to LAD Estimator Asymptotics

1991 ◽  
Vol 7 (4) ◽  
pp. 450-463 ◽  
Author(s):  
P.C.B. Phillips
Keyword(s):  
Asymptotic Expansion ◽  
Regression Model ◽  
Taylor Series ◽  
Asymptotic Theory ◽  
Random Variables ◽  
Generalized Functions ◽  
Infinite Variance ◽  
Series Expansions ◽  
Linear Functionals ◽  
Taylor Series Expansions

Using generalized functions of random variables and generalized Taylor series expansions, we provide quick demonstrations of the asymptotic theory for the LAD estimator in a regression model setting. The approach is justified by the smoothing that is delivered in the limit by the asymptotics, whereby the generalized functions are forced to appear as linear functionals wherein they become real valued. Models with fixed and random regressors, and autoregressions with infinite variance errors are studied. Some new analytic results are obtained including an asymptotic expansion of the distribution of the LAD estimator.

scholarly journals Some Difference Equations for Srivastava’s λ-Generalized Hurwitz–Lerch Zeta Functions with Applications

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 311 ◽  
Author(s):  
Asifa Tassaddiq
Keyword(s):  
Integral Representation ◽  
Difference Equations ◽  
Zeta Functions ◽  
Numerical Computations ◽  
Direct Evaluation ◽  
Mellin Transforms ◽  
The Family

In this article, we establish some new difference equations for the family of λ-generalized Hurwitz–Lerch zeta functions. These difference equations proved worthwhile to study these newly defined functions in terms of simpler functions. Several authors investigated such functions and their analytic properties, but no work has been reported for an estimation of their values. We perform some numerical computations to evaluate these functions for different values of the involved parameters. It is shown that the direct evaluation of involved integrals is not possible for the large values of parameter s; nevertheless, using our new difference equations, we can evaluate these functions for the large values of s. It is worth mentioning that for the small values of this parameter, our results are 100% accurate with the directly computed results using their integral representation. Difference equations so obtained are also useful for the computation of some new integrals of products of λ-generalized Hurwitz–Lerch zeta functions and verified to be consistent with the existing results. A derivative property of Mellin transforms proved fundamental to present this investigation.

scholarly journals A Method for the Generation of Various Ghost Correction Algorithms—the Example of the Positivity Method and the Exponential Method

1991 ◽  
Vol 13 (4) ◽  
pp. 199-212 ◽  
Author(s):  
P. Van Houtte
Keyword(s):  
Pole Figure ◽  
Taylor Series ◽  
The Other ◽  
New Method ◽  
Series Expansions ◽  
Theoretical Scheme ◽  
Taylor Series Expansions ◽  
Exponential Method ◽  
Pole Figure Data

A theoretical strategy is presented that can derive the algorithms of several existing ghost correction methods. The examples of the positivity method and the “GHOST” method are elaborated. A new method is derived as well: the “exponential” method. It can successfully replace the quadratic method as a method that yields an exactly non-negative complete C.O.D.F. from pole figure data. The theoretical scheme that can generate all these algorithms makes use of the fact, that several parameter sets can be defined in order to describe a C.O.D.F. The parameters of one set are then functions of those of the other. The algorithms are derived from Taylor series expansions of these functions.

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