scholarly journals Integral formulas for Chebyshev polynomials and the error term of interpolatory quadrature formulae for analytic functions

2006 ◽  
Vol 75 (255) ◽  
pp. 1217-1232 ◽  
Author(s):  
Sotirios E. Notaris
Keyword(s):  
Chebyshev Polynomials ◽  
Analytic Functions ◽  
Error Term ◽  
Quadrature Formulae ◽  
Integral Formulas ◽  
Interpolatory Quadrature Formulae ◽  
Interpolatory Quadrature

scholarly journals On a Class of Distributions Stable Under Random Summation

2012 ◽  
Vol 49 (02) ◽  
pp. 303-318 ◽  
Author(s):  
L. B. Klebanov ◽  
A. V. Kakosyan ◽  
S. T. Rachev ◽  
G. Temnov
Keyword(s):  
Normal Distribution ◽  
Generating Function ◽  
Chebyshev Polynomials ◽  
Generating Functions ◽  
Analytic Functions ◽  
Random Variable ◽  
Random Summation ◽  
The Stability ◽  
Rational Generating Functions ◽  
Family Of Distributions

We study a family of distributions that satisfy the stability-under-addition property, provided that the number ν of random variables in a sum is also a random variable. We call the corresponding property ν-stability and investigate the situation when the semigroup generated by the generating function of ν is commutative. Using results from the theory of iterations of analytic functions, we describe ν-stable distributions generated by summations with rational generating functions. A new case in this class of distributions arises when generating functions are linked with Chebyshev polynomials. The analogue of normal distribution corresponds to the hyperbolic secant distribution.

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