Geodesic
Accuracy of the approximation of the characteristic functions by polynomials
Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part IX, Tome 142 (1985), pp. 141-144 
L. V. Rozovskii. Accuracy of the approximation of the characteristic functions by polynomials. Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part IX, Tome 142 (1985), pp. 141-144. http://geodesic.mathdoc.fr/item/ZNSL_1985_142_a14/
@article{ZNSL_1985_142_a14,
     author = {L. V. Rozovskii},
     title = {Accuracy of the approximation of the characteristic functions by polynomials},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {141--144},
     year = {1985},
     volume = {142},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1985_142_a14/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In the paper one obtains a series of statements allowing us to estimate the accuracy of the approximation of the characteristic function $f(t)=\int e^{itx}dV(x)$ by a polynomial of integer powers of $it$. For example, $$ C_1\Gamma(b)\le\sup_{|t|\le b}|f(t)-1-\sum_{l=1}^{2M-1}\frac{(it)^l}{l!}d_l|\le C_2\Gamma(b) $$ where the positive constants $$, $$ depend only on $M$, $M\ge1$ is an integer, $b>0,$ $$ \Gamma(b)=\int_{-\infty}^{\infty}\min\Big(1, (xb)^{2M}\Big)dV(x)+\max_{1\le l\le2M}b^2|d_l-\int_{|xb|\le1}x^ldV(x)|. $$