Limit theorems for numbers satisfying a class of triangular arrays
Keyword(s):
The paper extends the investigations of limit theorems for numbers satisfying a class of triangular arrays, defined by a bivariate linear recurrence with bivariate linear coefficients. We obtain the partial differential equation and special analytical expressions for the numbers using a semi-exponential generating function. We apply the results to prove the asymptotic normality of special classes of the numbers and specify the convergence rate to the limiting distribution. We demonstrate that the limiting distribution is not always Gaussian.
1982 ◽
Vol 91
(3-4)
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pp. 205-212
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2015 ◽
Vol 44
(2)
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pp. 312-320
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2007 ◽
Vol 10
(7)
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pp. 657-676
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2011 ◽
Vol 31
(3)
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pp. 753-756
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2010 ◽
Vol 12
(2)
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pp. 125-131
2000 ◽
Vol 42
(3-4)
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pp. 417-422
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2019 ◽
Vol 677
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pp. 052066