scholarly journals Extension of generalized integro-exponential function and its application in study of Chen distribution

2017 ◽  
Vol 11 (2) ◽  
pp. 434-450 ◽  
Author(s):  
Tibor Pogány ◽  
Gauss Cordeiro ◽  
Muhammad Tahir ◽  
Hari Srivastava
Keyword(s):  
Power Series ◽  
Closed Form ◽  
Series Expansion ◽  
Exponential Function ◽  
Generating Functions ◽  
Power Series Expansion ◽  
Quantile Function ◽  
Mathematical Properties ◽  
Lifetime Model ◽  
Two Parameter

In 2000 Chen introduced a two-parameter lifetime model and has reported only a few mathematical properties moments, quantile and generating functions, among others. In this article, we derive a power series expansion for newly introduced real upper parameter generalized integro-exponential function Eps(z) extending certain Milgram's findings. By our novel results we derive closed-form expressions for the moments, generating function, R?nyi entropy and power series for the quantile function of the Chen distribution.

Design of a Variable Fractional Delay Filter Using Comprehensive Least Square Method Encompassing All Delay Values

2015 ◽  
Vol 24 (08) ◽  
pp. 1550116 ◽  
Author(s):  
Manjeet Kumar ◽  
Tarun Kumar Rawat
Keyword(s):  
Power Series ◽  
Cost Function ◽  
Frequency Response ◽  
Series Expansion ◽  
Exponential Function ◽  
Power Series Expansion ◽  
Least Square Method ◽  
Least Square ◽  
Fractional Delay ◽  
Fractional Delay Filter

The work presented in this paper is concerned with the designing of a variable fractional delay (VFD) FIR filter using least square method encompassing all delay values p. First, the frequency response, e-jωp, of the VFD filter is approximated using power series expansion of an exponential function and then, it is represented in terms of frequency response of the differentiator. Next, the proposed least square method adopts a novel cost function which includes all the fractional delay values. Finally, design and application examples are given to illustrate that the proposed least square method have better design accuracy and significantly reduction in magnitude error with the same degree of complexity than existing least square methods.

scholarly journals Identities Involving the Fourth-Order Linear Recurrence Sequence

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1476 ◽  
Author(s):  
Lan Qi ◽  
Zhuoyu Chen
Keyword(s):  
Power Series ◽  
Series Expansion ◽  
Generating Function ◽  
Fourth Order ◽  
Power Series Expansion ◽  
Linear Recurrence ◽  
Recurrence Sequence ◽  
Order Linear ◽  
Elementary Methods ◽  
Linear Recurrence Sequence

In this paper, we introduce the fourth-order linear recurrence sequence and its generating function and obtain the exact coefficient expression of the power series expansion using elementary methods and symmetric properties of the summation processes. At the same time, we establish some relations involving Tetranacci numbers and give some interesting identities.

Analytic Structure and Power-Series Expansion of the Jost Matrix

2012 ◽  
Vol 54 (5-6) ◽  
pp. 673-683
Author(s):  
S. A. Rakityansky ◽  
N. Elander
Keyword(s):  
Power Series ◽  
Series Expansion ◽  
Power Series Expansion ◽  
Analytic Structure
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