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

R. B. Paris

Research output: Contribution to journal › Article

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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 languageEnglish
Pages (from-to)231-244
Number of pages14
JournalMathematica Æterna
Volume5
Issue number2
Publication statusPublished - 2015

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Gauss Hypergeometric Function
Unit
Term
Factorial
Excess

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Paris, R. B. / The expansion of a finite number of terms of the Gauss hypergeometric function of unit argument and the Landau constants. In: Mathematica Æterna. 2015 ; Vol. 5, No. 2. pp. 231-244.
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Paris, RB 2015, 'The expansion of a finite number of terms of the Gauss hypergeometric function of unit argument and the Landau constants', 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.

In: Mathematica Æterna, Vol. 5, No. 2, 2015, p. 231-244.

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 -

Paris RB. The expansion of a finite number of terms of the Gauss hypergeometric function of unit argument and the Landau constants. Mathematica Æterna. 2015;5(2):231-244.

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