Expansions of the Kurepa Functions
Publications de l'Institut Mathématique, _N_S_57 (1995) no. 71, p. 81
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The Taylor series expansions of the Kurepa function
$K(a+z)$, $a\ge 0$, and numerical determination of their coefficients
$b_\nu(a)$ for $a=0$ and $a=1$ are given. An asymptotic behaviour of
$b_\nu(a)$ as well as that $|b_\nu(a)/b_{\nu+1}(a)|\sim a+1$, when
$\nu\to\infty$, are shown. Using this fact, a transformation of series
with much faster convergence is done. Numerical values of coefficients
in such a transformed series for $a=0$ and $a=1$ are given with $30$
decimal digits. Also, the Chebyshev expansions of $K(1+z)$ and
$1/K(1+z)$ are obtained.
Classification :
33B15 64D20
Gradimir V. Milovanović. Expansions of the Kurepa Functions. Publications de l'Institut Mathématique, _N_S_57 (1995) no. 71, p. 81 . http://geodesic.mathdoc.fr/item/PIM_1995_N_S_57_71_a8/
@article{PIM_1995_N_S_57_71_a8,
author = {Gradimir V. Milovanovi\'c},
title = {Expansions of the {Kurepa} {Functions}},
journal = {Publications de l'Institut Math\'ematique},
pages = {81 },
year = {1995},
volume = {_N_S_57},
number = {71},
language = {en},
url = {http://geodesic.mathdoc.fr/item/PIM_1995_N_S_57_71_a8/}
}