Finding Solutions to Equations for the Longitudinal Components of an Electromagnetic Field in a Biisotropic Medium in the Neighborhood of a Regular Singular Point as Generalized Power Series

2004 ◽  
Vol 47 (5) ◽  
pp. 525-533
Author(s):  
V. A. Mescheryakov ◽  
A. E. Mudrov ◽  
G. A. Red'kin ◽  
A. A. Zhukov
Keyword(s):  
Electromagnetic Field ◽  
Singular Point ◽  
Power Series ◽  
Regular Singular Point ◽  
Solutions To Equations ◽  
Generalized Power Series ◽  
Biisotropic Medium

On the Distribution of Sum of Independent Positive Binomial Variables

1970 ◽  
Vol 13 (1) ◽  
pp. 151-152 ◽  
Author(s):  
J. C. Ahuja
Keyword(s):  
Power Series ◽  
Inversion Formula ◽  
Probability Function ◽  
Random Variables ◽  
Random Variable ◽  
Characteristic Functions ◽  
Binomial Probability ◽  
Generalized Power Series ◽  
Alternative Derivation ◽  
Image Position

Let X1, X2, …, Xn be n independent and identically distributed random variables having the positive binomial probability function1where 0 < p < 1, and T = {1, 2, …, N}. Define their sum as Y=X1 + X2 + … +Xn. The distribution of the random variable Y has been obtained by Malik [2] using the inversion formula for characteristic functions. It appears that his result needs some correction. The purpose of this note is to give an alternative derivation of the distribution of Y by applying one of the results, established by Patil [3], for the generalized power series distribution.

The Characteristic of Power Series and its Sum Function on the Convergence Circle

2013 ◽  
Vol 821-822 ◽  
pp. 1434-1437
Author(s):  
Sheng Ma ◽  
Qin Jiang
Keyword(s):  
Singular Point ◽  
Power Series ◽  
The Relationship

In the paper, the specific issues is discussed whether or not the points on the convergence circle are the singular point of a sum function of a class of power series. Whats more, the relationship between divergence of the power series on the convergence circle and the pole of its function on the convergence circle is explored. And a new result is obtained that there exists the pole of its function on the convergence circle, the power series has the characteristic of everywhere divergence on the convergence circle.

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