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A continued fraction approximation of the gamma function
Abstract The aim of this work is to construct a continued fraction approximation of the gamma function. Some inequalities are established.
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  • 6
Product Approximations via Asymptotic Integration
  • C. Mortici
  • Computer Science, Mathematics
  • Am. Math. Mon.
  • 1 May 2010
  • 141
  • 5
The natural approach of Wilker-Cusa-Huygens inequalities
The aim of this paper is to provide a natural approach of Wilker-Cusa-Huygens inequalities. This new approach permits us to give new proofs then to refine much these inequalities and we are convincedExpand
  • 76
  • 5
  • PDF
New approximations of the gamma function in terms of the digamma function
  • C. Mortici
  • Mathematics, Computer Science
  • Appl. Math. Lett.
  • 2010
TLDR
We find the best approximations Gb∗,c∗ and Gb#,c# , where b∗ > b# are the real roots of the polynomial 18b4 + 24b3 . Expand
  • 81
  • 4
  • PDF
On the harmonic number expansion by Ramanujan
AbstractLet γ=0.577215664… denote the Euler-Mascheroni constant, and let the sequences The main aim of this paper is to find the values r, s, t, a, b, c and d which provide the fastest sequencesExpand
  • 20
  • 4
Error estimates of Ramanujan-type series
The aim of this paper is to establish some inequalities related to Ramanujan-type approximation series of the constant π and other classical constants such as Apéry’s constant and Catalan’s constant.
  • 5
  • 4
New sequence converging towards the Euler-Mascheroni constant
TLDR
We propose new sequences containing a modified logarithmic term which converge to the Euler-Mascheroni constant faster than sequences known from the literature. Expand
  • 82
  • 3
Sharp inequalities related to Gosper's formula
Abstract The purpose of this Note is to construct a new type of Stirling series, which extends the Gosper's formula for big factorials. New sharp inequalities for the gamma and digamma functions areExpand
  • 45
  • 3
A new Stirling series as continued fraction
  • C. Mortici
  • Mathematics, Computer Science
  • Numerical Algorithms
  • 2010
AbstractWe introduce the following new Stirling series $$ n!\sim \sqrt{2\pi n}\left( \frac{n}{e}\right) ^{n}\exp \frac{1}{12n+\frac{Expand
  • 63
  • 3
Sharp bounds of the Landau constants
  • C. Mortici
  • Computer Science, Mathematics
  • Math. Comput.
  • 1 May 2011
TLDR
We improve the upper bound in the following way, that also shows that the constant 3=4 is the best possible. Expand
  • 21
  • 3
  • PDF
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