### Abstract

We obtain convergent inverse factorial expansions for the sum S

*n*(*a*,*b*;*c*) of the first*n*≥ 1 terms of the Gauss hypergeometric function_{2}F_{1}(*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 |

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## Cite this

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.