OPTIMIZING THE RATE OF CONVERGENCE IN SOME NEW CLASSES OF SEQUENCES CONVERGENT TO EULER'S CONSTANT
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Publication:3406716
DOI10.1142/S0219530510001539zbMath1185.26047OpenAlexW2057855454MaRDI QIDQ3406716
Publication date: 19 February 2010
Published in: Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1142/s0219530510001539
Inequalities for sums, series and integrals (26D15) Rate of convergence, degree of approximation (41A25) Asymptotic expansions of solutions to ordinary differential equations (34E05) Evaluation of number-theoretic constants (11Y60)
Related Items (35)
The best rational remainders in the Stirling formula ⋮ Optimal bounds for the generalized Euler-Mascheroni constant ⋮ A series of sequences convergent to Euler's constant ⋮ Some new improved classes of convergence towards Euler's constant ⋮ Some new sequences and inequalities related to Euler's constant ⋮ New sequences with continued fraction towards Euler's constant ⋮ Improved convergence towards generalized Euler-Mascheroni constant ⋮ A new quicker sequence convergent to Euler's constant ⋮ Some quicker classes of sequences convergent to Euler's constant ⋮ Asymptotic expansions for the psi function and the Euler-Mascheroni constant ⋮ Ramanujan formula for the generalized Stirling approximation ⋮ On new sequences converging towards the Ioachimescu's constant ⋮ New approximation formulas for evaluating the ratio of gamma functions ⋮ Estimating gamma function by digamma function ⋮ A new Stirling series as continued fraction ⋮ On Ramanujan's large argument formula for the gamma function ⋮ A continued fraction approximation of the gamma function ⋮ Improved asymptotic formulas for the gamma function ⋮ Monotonicity properties of the volume of the unit ball in \({\mathbb{R}^{n}}\) ⋮ Some new continued fraction approximation of Euler's constant ⋮ New quicker sequences and inequalities with continued fraction towards Euler's constant ⋮ Some quicker continued fraction approximations and inequalities towards Euler's constant ⋮ Accurate Estimates of the Gamma Function Involving the PSI Function ⋮ Some new convergent sequences and inequalities of Euler's constant ⋮ A substantial improvement of the Stirling formula ⋮ Ramanujan's estimate for the gamma function via monotonicity arguments ⋮ Best estimates of the generalized Stirling formula ⋮ Sharp inequalities related to Gosper's formula ⋮ A class of integral approximations for the factorial function ⋮ On new sequences converging towards the Euler-Mascheroni constant ⋮ Inequalities and asymptotic expansions for the psi function and the Euler-Mascheroni constant ⋮ A New Asymptotic Series and Estimates Related to Euler Mascheroni Constant ⋮ Approximations of the generalized-Euler-constant function and the generalized Somos' quadratic recurrence constant ⋮ New approximations of the gamma function in terms of the digamma function ⋮ Continued fraction inequalities for the Euler-Mascheroni constant
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