Bases formed of successive primitives
Matematičeskie zametki, Tome 3 (1968) no. 3, pp. 237-246
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Necessary and sufficient conditions are found in order for the system of successive primitives
$$
\biggl\{F_n(z)=\sum_{k=0}^\infty\frac{a+_{k-n}}{k!}z^k\biggr\},\quad n=0,1,2,\dots,
$$
generated by the integer-valued function $F_0(z)=\sum_{k=0}^\infty\frac{a_{k_{zk}}}{k!}$ growth no higher than first order of the normal type $\sigma(F_0(z)\in[1,\sigma]$, to form a quasi-power basis in the class $[1;\sigma]$.
@article{MZM_1968_3_3_a0,
author = {Yu. A. Kaz'min},
title = {Bases formed of successive primitives},
journal = {Matemati\v{c}eskie zametki},
pages = {237--246},
publisher = {mathdoc},
volume = {3},
number = {3},
year = {1968},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1968_3_3_a0/}
}
Yu. A. Kaz'min. Bases formed of successive primitives. Matematičeskie zametki, Tome 3 (1968) no. 3, pp. 237-246. http://geodesic.mathdoc.fr/item/MZM_1968_3_3_a0/