PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 57(71) (dedicated to Djuro Kurepa), pp. 8190 (1995) 

Expansions of the Kurepa functionsGradimir Milovanovi\'cElektronski fakultet, Nis, YugoslaviaAbstract: 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 (MSC2000): 33B15, 64D20 Full text of the article:
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© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
