Geodesic
Expansions of the Kurepa Functions
Publications de l'Institut Mathématique, _N_S_57 (1995) no. 71, p. 81

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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 
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     author = {Gradimir V. Milovanovi\'c},
     title = {Expansions of the {Kurepa} {Functions}},
     journal = {Publications de l'Institut Math\'ematique},
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     publisher = {mathdoc},
     volume = {_N_S_57},
     number = {71},
     year = {1995},
     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/