Abstract
We obtain convergent inverse factorial expansions for the sum Sn(a, b; c) of the first n ≥ 1 terms of the Gauss hypergeometric function 2F1(a, b; c; 1) of unit argument. The form of these expansions depends on the location of the parametric excess s := c−a−b in the complex s-plane. The leading behaviour as n → ∞ agrees with previous results in the literature. The case a = b = 1/2 , c = 1 corresponds to the Landau contants for which an expansion is obtained.
Original language | English |
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Pages (from-to) | 231-244 |
Number of pages | 14 |
Journal | Mathematica Æterna |
Volume | 5 |
Issue number | 2 |
Publication status | Published - 2015 |