scholarly journals Reduce procedures for the manipulation of generalized power series

1986 ◽  
Vol 39 (2) ◽  
pp. 267-284 ◽  
Author(s):  
E. Feldmar ◽  
K.S. Kölbig
Keyword(s):  
Power Series ◽  
Generalized Power Series

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.

scholarly journals Special Properties of Generalized Power Series

1995 ◽  
Vol 173 (3) ◽  
pp. 566-586 ◽  
Author(s):  
P. Ribenboim
Keyword(s):  
Power Series ◽  
Generalized Power Series

On semilocal, Bézout and distributive generalized power series rings

2015 ◽  
Vol 25 (05) ◽  
pp. 725-744 ◽  
Author(s):  
Ryszard Mazurek ◽  
Michał Ziembowski
Keyword(s):  
Power Series ◽  
Neumann Series ◽  
Polynomial Rings ◽  
Group Rings ◽  
Power Series Ring ◽  
Generalized Power Series ◽  
Series Ring ◽  
Ordered Monoid ◽  
Power Series Rings ◽  
Totally Ordered Monoid

Let R be a ring, and let S be a strictly ordered monoid. The generalized power series ring R[[S]] is a common generalization of polynomial rings, Laurent polynomial rings, power series rings, Laurent series rings, Mal'cev–Neumann series rings, monoid rings and group rings. In this paper, we examine which conditions on R and S are necessary and which are sufficient for the generalized power series ring R[[S]] to be semilocal right Bézout or semilocal right distributive. In the case where S is a strictly totally ordered monoid we characterize generalized power series rings R[[S]] that are semilocal right distributive or semilocal right Bézout (the latter under the additional assumption that S is not a group).

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