Bases formed of successive primitives |
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Authors: | Yu A Kaz'min |
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Institution: | 1. M. V. Lomonosov Moscow State University, USSR
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Abstract: | Necessary and sufficient conditions are found in order for the system of successive primitives $$\left\{ {F_n (z) = \sum\nolimits_{k = 0}^\infty {\frac{{a_{k - n} }}{{k!}}z^k } } \right\}, n = 0,1,2, ...,$$ generated by the integer-valued function \(F_n (z) = \sum\nolimits_{k = 0}^\infty {\frac{{a_k }}{{k!}}zk} \) of growth no higher than first order of the normal typeσ(F0(z) ε 1;σ] to form a quasi-power basis in the class 1; σ]. |
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