Closed-form design of maximally flat FIR Hilbert transformers, differentiators, and fractional delayers by power series expansion

2001 ◽  
Vol 48 (4) ◽  
pp. 389-398 ◽  
Author(s):  
Soo-Chang Pei ◽  
Peng-Hua Wang
Keyword(s):  
Power Series ◽  
Closed Form ◽  
Series Expansion ◽  
Power Series Expansion ◽  
Form Design

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.

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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