A continued fraction approximation of the gamma function

From MaRDI portal
Publication:1947301

DOI10.1016/j.jmaa.2012.11.023zbMath1333.40001OpenAlexW2083868407MaRDI QIDQ1947301

Cristinel Mortici

Publication date: 22 April 2013

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2012.11.023




Related Items (71)

A more accurate approximation for the gamma functionA series of sequences convergent to Euler's constantWindschitl type approximation formulas for the gamma functionComplete characterizations of the gamma functionAsymptotic expansions of the gamma function related to Windschitl's formulaSome new improved classes of convergence towards Euler's constantOn Stirling's formula remainderSome new asymptotic approximations of the gamma function based on Nemes' formula, Ramanujan's formula and Burnside's formulaEstimates of the function and quotient by Minc-SathreSome new exponential-function estimates of the Somos' quadratic recurrence constantSome new sequences and inequalities related to Euler's constantNew sequences with continued fraction towards Euler's constantA quicker continued fraction approximation of the gamma function related to the Windschitl's formulaA new general asymptotic formula and inequalities involving the volume of the unit ballA new quicker sequence convergent to Euler's constantA generated approximation related to Burnside's formulaInequalities and asymptotic expansions associated with the Ramanujan and nemes formulas for the gamma functionSome quicker classes of sequences convergent to Euler's constantSome quicker approximations and inequalities of the Wallis ratio by continued fractionSome new approximations and inequalities of the sequence \((1+1/n)^n\) and improvements of Carleman's inequalityAsymptotic expansions for the psi function and the Euler-Mascheroni constantContinued fraction approximation for the gamma function based on the tri-gamma functionSome asymptotic formulas and inequalities about gamma and psi functions based on continued fractionsImproved convergence towards Glaisher-Kinkelin's and Bendersky-Adamchik's constantsA kind of new continued fraction approximation of gamma function based on Mortici's formulaImproved approximation formulas and inequalities for the Wallis ratioA generated approximation of the gamma function related to Windschitl's formulaA new asymptotic expansion and some inequalities for the gamma functionApproximation for the gamma function via the tri-gamma functionSome new quicker approximations of Glaisher-Kinkelin's and Bendersky-Adamchik's constantsA new fast asymptotic series for the gamma functionSharp inequalities and asymptotic expansions for the gamma functionInequalities, asymptotic expansions and completely monotonic functions related to the gamma functionOn the Ramanujan-Lodge harmonic number expansionOptimizing the coefficients of the Ramanujan expansionSome inequalities associated to the ratio of Pochhammer k-symbolSome new quicker continued fraction approximations for the gamma function related to the Nemes' formulaSome new continued fraction approximation of Euler's constantSome inequalities for the trigamma function in terms of the digamma functionMultiple-correction and continued fraction approximationA quicker approximation of the gamma function towards the Windschitl's formula by continued fractionMonotonicity properties, inequalities and asymptotic expansions associated with the gamma functionTwo asymptotic expansions for gamma function developed by Windschitl's formulaCompletely monotonic functions and inequalities associated to some ratios of the Pochhammer \(k\)-symbolOn the asymptotic expansions of the gamma function related to the Nemes, Gosper and Burnside formulasContinued fraction approximation and inequality of the gamma functionNew quicker sequences and inequalities with continued fraction towards Euler's constantNew asymptotic formulas and inequalities for the gamma function based on continued fractionsSome new convergent sequences of Glaisher-Kinkelin's and Bendersky-Adamchik's constantsSome quicker continued fraction approximations and inequalities towards Euler's constantContinued fraction approximation for the gamma function by the tri-gamma functionA new approximation of the gamma function by expanding the Windschitl's formulaContinued fractions and inequalities about \(\left( 1+\frac{1}{x}\right)^x\)Continued fraction approximations and inequalities for the gamma function by BurnsidePadé approximant related to asymptotics for the gamma functionSome new convergent sequences and inequalities of Euler's constantInequalities and asymptotic expansions for the gamma functionA new sharp approximation for the gamma function related to Burnside's formulaA generated approximation related to Gosper's formula and Ramanujan's formulaSharp approximation formulas and inequalities for the Wallis ratio by continued fractionSome new approximations of Glaisher-Kinkelin's and Bendersky-Adamchik's constants by continued fractionUnified approaches to the approximations of the gamma functionInequalities and asymptotic expansions for the psi function and the Euler-Mascheroni constantImproved asymptotic formula and inequalities for the ratio of Pochhammer \(k\)-symbolAsymptotic expansions for the gamma functionA general asymptotic formula of the gamma function based on the Burnside's formulaEmergence of new category of continued fractions from the Sturm-Liouville problem and the Schrödinger equationMonotonicity, convexity, and complete monotonicity of two functions related to the gamma functionNew inequalities for gamma and digamma functionsSome new continued fraction estimates of the Somos' quadratic recurrence constantContinued fraction inequalities for the Euler-Mascheroni constant



Cites Work


This page was built for publication: A continued fraction approximation of the gamma function