scholarly journals Some families of generalized Mathieu-type power series, associated probability distributions and related inequalities involving complete monotonicity and log-convexity

2017 ◽  
pp. 973-986 ◽  
Author(s):  
Živorad Tomovski ◽  
Khaled Mehrez
Keyword(s):  
Power Series ◽  
Probability Distributions ◽  
Complete Monotonicity ◽  
Type Power

Integral expressions for Mathieu-type power series and for the Butzer-Flocke-Hauss Ω-function

2011 ◽  
Vol 14 (4) ◽  
Author(s):  
Živorad Tomovski ◽  
Tibor Pogány
Keyword(s):  
Power Series ◽  
Fractional Order ◽  
Integral Representations ◽  
Type Power

AbstractIn this paper several integral representations for the generalized fractional order Mathieu type power series $S_\mu (r;x) = \sum\limits_{n = 1}^\infty {\frac{{2nx^n }} {{(n^2 + r^2 )^{\mu + 1} }}(r \in \mathbb{R},\mu > 0,|x| \leqslant 1)} $ are presented. Also new integral expressions are derived for the Butzer-Flocke-Hauss (BFH) complete Omega function.

Burmann-series distributions and approximation operators

2005 ◽  
Vol 42 (4) ◽  
pp. 355-369
Author(s):  
J. P. King
Keyword(s):  
Power Series ◽  
Probability Distributions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Approximation Operators ◽  
Real Functions

Burmann series are used to give probability distributions which generalize the known class of distributions given by power series. Positive linear operators associated with Burmann-series distribution are described. Convergence of these operators to continuous real functions is studied. Examples are discussed.

The Orthogonal Polynomials of Power Series Probability Distributions and Their Uses

Biometrika ◽  
1966 ◽  
Vol 53 (1/2) ◽  
pp. 121
Author(s):  
D. F. I van Heerden ◽  
H. T. Gonin
Keyword(s):  
Power Series ◽  
Orthogonal Polynomials ◽  
Probability Distributions

scholarly journals From Invariance Under Binomial Thinning to Unification of the Cauchy and the Gołąb–Schinzel-Type Equations

2021 ◽  
Vol 76 (4) ◽  
Author(s):  
Karol Baron ◽  
Jacek Wesolowski
Keyword(s):  
Power Series ◽  
Functional Equations ◽  
Probability Distributions ◽  
Binomial Thinning ◽  
Additive Form

AbstractWe point out to a connection between a problem of invariance of power series families of probability distributions under binomial thinning and functional equations which generalize both the Cauchy and an additive form of the Gołąb–Schinzel equation. We solve these equations in several settings with no or mild regularity assumptions imposed on unknown functions.

scholarly journals The T–R {Y} power series family of probability distributions

2020 ◽  
Vol 28 (1) ◽  
Author(s):  
Patrick Osatohanmwen ◽  
Francis O. Oyegue ◽  
Sunday M. Ogbonmwan
Keyword(s):  
Power Series ◽  
Probability Distributions

Complemented infinite type power series subspaces of nuclear Fréchet spaces

1989 ◽  
Vol 283 (2) ◽  
pp. 193-202 ◽  
Author(s):  
A. Aytuna ◽  
J. Krone ◽  
T. Terzioğlu
Keyword(s):  
Power Series ◽  
Fréchet Spaces ◽  
Infinite Type ◽  
Type Power
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