Abstract
In this paper some fractional analogues of classical Pearson differential equations are explicitly solved. Limit transitions between the solutions are analyzed, providing a generalization of well-known transitions between the beta and gamma, and between the gamma and normal distributions. Finally, quasi-polynomials orthogonal with respect to these fractional analogues of the classical distributions are introduced, and some conjectures about their zeros are posed.
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Area, I., Losada, J. & Manintchap, A. On Some Fractional Pearson Equations. FCAA 18, 1164–1178 (2015). https://doi.org/10.1515/fca-2015-0067
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DOI: https://doi.org/10.1515/fca-2015-0067