scholarly journals Euler integral and perihelion librations

2020 ◽  
Vol 40 (12) ◽  
pp. 6919-6943 ◽  
Author(s):  
Gabriella Pinzari ◽  
Keyword(s):  
Euler Integral

scholarly journals Fractional operators with generalized Mittag-Leffler k-function

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Shahid Mubeen ◽  
Rana Safdar Ali
Keyword(s):  
Hypergeometric Function ◽  
Hypergeometric Functions ◽  
Integral Transforms ◽  
Fractional Integrals ◽  
Fractional Operators ◽  
Euler Integral ◽  
K Function ◽  
Generalized Wright Hypergeometric Function

AbstractIn this paper, our main aim is to deal with two integral transforms involving the Gauss hypergeometric functions as their kernels. We prove some composition formulas for such generalized fractional integrals with Mittag-Leffler k-function. The results are established in terms of the generalized Wright hypergeometric function. The Euler integral k-transformation for Mittag-Leffler k-functions has also been developed.

Inversion of Euler integral transforms with applications to sensor data

2011 ◽  
Vol 27 (12) ◽  
pp. 124001 ◽  
Author(s):  
Yuliy Baryshnikov ◽  
Robert Ghrist ◽  
David Lipsky
Keyword(s):  
Integral Transforms ◽  
Sensor Data ◽  
Euler Integral

Algebraic Evaluations of Some Euler Integrals, Duplication Formulae for Appell's Hypergeometric Function F1, and Brownian Variations

2000 ◽  
Vol 52 (5) ◽  
pp. 961-981 ◽  
Author(s):  
Mourad E. H. Ismail ◽  
Jim Pitman
Keyword(s):  
Hypergeometric Function ◽  
Total Variation ◽  
Brownian Bridge ◽  
Mean Square ◽  
Elementary Functions ◽  
Euler Integral

AbstractExplicit evaluations of the symmetric Euler integral are obtained for some particular functions f. These evaluations are related to duplication formulae for Appell’s hypergeometric function F1 which give reductions of F1(α, β, β, 2α, y, z) in terms of more elementary functions for arbitrary β with z = y/(y − 1) and for β = α + 1/2 with arbitrary y, z. These duplication formulae generalize the evaluations of some symmetric Euler integrals implied by the following result: if a standard Brownian bridge is sampled at time 0, time 1, and at n independent randomtimes with uniformdistribution on [0, 1], then the broken line approximation to the bridge obtained from these n + 2 values has a total variation whose mean square is n(n + 1)/(2n + 1).

scholarly journals EULER INTEGRATION OF GAUSSIAN RANDOM FIELDS AND PERSISTENT HOMOLOGY

2012 ◽  
Vol 04 (01) ◽  
pp. 49-70 ◽  
Author(s):  
OMER BOBROWSKI ◽  
MATTHEW STROM BORMAN
Keyword(s):  
Random Field ◽  
Euler Characteristic ◽  
Persistent Homology ◽  
Gaussian Random Field ◽  
Gaussian Random Fields ◽  
Closed Form Expression ◽  
Form Expression ◽  
Kinematic Formula ◽  
Euler Integral ◽  
The Relationship

In this paper we extend the notion of the Euler characteristic to persistent homology and give the relationship between the Euler integral of a function and the Euler characteristic of the function's persistent homology. We then proceed to compute the expected Euler integral of a Gaussian random field using the Gaussian kinematic formula and obtain a simple closed form expression. This results in the first explicitly computable mean of a quantitative descriptor for the persistent homology of a Gaussian random field.

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