### Abstract

*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 |
---|---|

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

*Mathematica Æterna*,

*5*(2), 231-244.

}

*Mathematica Æterna*, vol. 5, no. 2, pp. 231-244.

**The expansion of a finite number of terms of the Gauss hypergeometric function of unit argument and the Landau constants.** / Paris, R. B.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The expansion of a finite number of terms of the Gauss hypergeometric function of unit argument and the Landau constants

AU - Paris, R. B.

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

M3 - Article

VL - 5

SP - 231

EP - 244

JO - Mathematica Æterna

JF - Mathematica Æterna

SN - 1314-3344

IS - 2

ER -