Linearization of the Product οf Orthogonal Polynomials

Author(s):  
Richard Askey
2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Rabia Aktaş ◽  
Iván Area ◽  
Esra Güldoğan

Author(s):  
Giacomo Ascione ◽  
Nikolai Leonenko ◽  
Enrica Pirozzi

AbstractIn this paper, we study strong solutions of some non-local difference–differential equations linked to a class of birth–death processes arising as discrete approximations of Pearson diffusions by means of a spectral decomposition in terms of orthogonal polynomials and eigenfunctions of some non-local derivatives. Moreover, we give a stochastic representation of such solutions in terms of time-changed birth–death processes and study their invariant and their limit distribution. Finally, we describe the correlation structure of the aforementioned time-changed birth–death processes.


IEEE Access ◽  
2021 ◽  
Vol 9 ◽  
pp. 59675-59691
Author(s):  
Kundan Kumar ◽  
Shovan Bhaumik ◽  
Paresh Date

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