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Closed Form Summation for Classical Distributions: Variations on Theme of De Moivre
Binomial distribution Stirling's formula his- tory of probability Pearson curves Stein's identity mean absolute deviation.
2015/7/14
De Moivre gave a simple closed form expression for the mean
absolute deviation of the binomial distribution. Later authors showed
that similar closed form expressions hold for many of the other cl...
Hypergeometric summation representations of the Stieltjes constants
Riemann zeta function Stieltjes constants generalized hypergeometric function
2011/7/26
Hypergeometric summation representations of the Stieltjes constants.
The Algorithm Z and Ramanujan's 1ψ1 Summation
Algorithm Z Ramanujan's 1ψ1 summation bijection partition
2014/6/3
We use the Algortihm Z on partitions due to Zeilberger, in a variant form, to give a combinatorial proof of Ramanujan's 1ψ1 summation formula.
A Symbolic Summation Approach to Feynman Integral Calculus
Symbolic Summation Feynman Integral Calculus
2010/12/27
Given a Feynman parameter integral, depending on a single discrete variable $N$ and a real parameter $\epsilon$, we discuss a new algorithmic framework to compute the first coefficients of its Lauren...
A Symbolic Summation Approach to Feynman Integral Calculus
Symbolic Summation Feynman Integral Calculus
2010/12/27
Given a Feynman parameter integral, depending on a single discrete variable $N$ and a real parameter $\epsilon$, we discuss a new algorithmic framework to compute the first coefficients of its Laurent...
We generalize the standard Poisson summation formula for lattices so that it operates on the level of theta series, allowing us to introduce noninteger dimension parameters (using the dimensionally c...
Compactness properties of weighted summation operators on trees - the critical case
Metrics on trees operators on trees weighted summation operators
2010/12/6
The aim of this paper is to provide upper bounds for the entropy numbers of summation
operators on trees in a critical case. In a recent paper [10] we elaborated a framework of
weighted summation op...
An Inequality for the Asymmetry of Distributions and a Berry-Esseen Theorem for Random Summation
Random number of i.i.d. random variables Central limit theorem for random sums Asymmetry of distributions Berry-Esseen theorem for random sums
2008/7/2
An Inequality for the Asymmetry of Distributions and a Berry-Esseen Theorem for Random Summation.
On a Hybrid Family of Summation Integral Type Operators
Linear positive operators Summation-integral type operators Rate of convergence Asymptotic formula Error estimate Local direct results $K$-functional Modulus of smoothness Simultaneous approximation
2008/6/30
The present paper deals with the study of the mixed summation integral type operators having Szász and Baskakov basis functions in summation and integration respectively. Here we obtain the rate of po...
Rate of Convergence of Summation-Integral Type Operators with Derivatives Of Bounded Variation
Linear positive operators Bounded variation Total variation Rate of convergence
2008/6/27
Rate of Convergence of Summation-Integral Type Operators with Derivatives Of Bounded Variation.
On linear combination of two classes of triangle summation operators of Bernstein type
triangle summation operator of Bernstein type uniform convergence
2010/9/15
To improve the convergence properties of the Lagrange interpolation operators, Bernstein constructed two classes of operators. Subsequently, many experts generalized these operators, and acquired sign...
Finding the minimize summation for location of facility in a convex set with fuzzy data
Facilities location Norm Linear Programming
2010/9/15
In this paper we first show a model using L1-Norm for locating a facility in a convex set and then we use it for fuzzy data in linear programming problems and especial case of integer linear programmi...
The Hypervirial-Padé Summation Method Applied to the Anharmonic Oscillator
Anharmonic oscillator Schrodinger equation hypervirial theorems Padé summation method
2010/4/12
The energy eigenvalues of the anharmonic oscillator characterized by the cubic potential for various eigenstates are determined within the framework of the hypervirial-Padé summation method. For this ...
Summation and transformation formulas for elliptic hypergeometric series
Summation transformation formulas elliptic hypergeometric series
2010/10/29
Using matrix inversion and determinant evaluation techniques we prove several summation and transformation formulas for terminating, balanced, very-well-poised, elliptic hypergeometric series.