Geodesic
Expansions of the Kurepa Functions
Publications de l'Institut Mathématique, _N_S_57 (1995) no. 71, p. 81 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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 
@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/}
}
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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/