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 |
|---|---|
| Pages (from-to) | 231-244 |
| Number of pages | 14 |
| Journal | Mathematica Æterna |
| Volume | 5 |
| Issue number | 2 |
| Publication status | Published - 2015 |
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Paris, R. B. (2015). The expansion of a finite number of terms of the Gauss hypergeometric function of unit argument and the Landau constants. Mathematica Æterna, 5(2), 231-244.