Geodesic
On hyper-sums and hyper-products of progressions
Taurida Journal of Computer Science Theory and Mathematics, no. 1 (2020), pp. 19-31

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In the article we study properties of some sequences of numbers (so-called “hyper-sums” and “hyper-products”) which one can construct on the basis of given numerical sequence. We consider such sequences for arithmetic, geometric progressions and Fibonacci numbers. We obtain explicit formulas for its calculation and study problems of asymptotic behavior. As a main result, we prove new asymptotic formula for hyper-products of arithmetic progression that generalized Stirling's formula and asymptotic of super-factorial.
Keywords: sequence of numbers, hyper-sums, hyper-products, asymptotic, generalized Stirling's formula, super-factorial. 
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     author = {V. I. Voytitsky},
     title = {On hyper-sums and hyper-products of progressions},
     journal = {Taurida Journal of Computer Science Theory and Mathematics},
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     number = {1},
     year = {2020},
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     url = {http://geodesic.mathdoc.fr/item/TVIM_2020_1_a1/}
}
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V. I. Voytitsky. On hyper-sums and hyper-products of progressions. Taurida Journal of Computer Science Theory and Mathematics, no. 1 (2020), pp. 19-31. http://geodesic.mathdoc.fr/item/TVIM_2020_1_a1/