Very accurate estimates of the polygamma functions
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Publication:3589436
DOI10.3233/ASY-2010-0983zbMath1204.33003OpenAlexW1834531137MaRDI QIDQ3589436
Publication date: 20 September 2010
Published in: Asymptotic Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3233/asy-2010-0983
Related Items (53)
Logarithmically completely monotonic functions related to the \(q\)-gamma function and its applications ⋮ Some monotonicity properties and inequalities for the generalized digamma and polygamma functions ⋮ Asymptotic expansions of the gamma function related to Windschitl's formula ⋮ Some new improved classes of convergence towards Euler's constant ⋮ Some new asymptotic approximations of the gamma function based on Nemes' formula, Ramanujan's formula and Burnside's formula ⋮ Some best approximation formulas and inequalities for the Wallis ratio ⋮ Some new sequences and inequalities related to Euler's constant ⋮ New sequences with continued fraction towards Euler's constant ⋮ A quicker continued fraction approximation of the gamma function related to the Windschitl's formula ⋮ A new quicker sequence convergent to Euler's constant ⋮ A generated approximation related to Burnside's formula ⋮ Some quicker classes of sequences convergent to Euler's constant ⋮ Topics in Special Functions III ⋮ Improved convergence towards Glaisher-Kinkelin's and Bendersky-Adamchik's constants ⋮ The asymptotic series of the generalized Stirling formula ⋮ Estimating the digamma and trigamma functions by completely monotonicity arguments ⋮ A generated approximation of the gamma function related to Windschitl's formula ⋮ A new asymptotic expansion and some inequalities for the gamma function ⋮ Some new quicker approximations of Glaisher-Kinkelin's and Bendersky-Adamchik's constants ⋮ A new Stirling series as continued fraction ⋮ On Ramanujan's large argument formula for the gamma function ⋮ Sharp inequalities and asymptotic expansions for the gamma function ⋮ The $\beta$-Delaunay tessellation III: Kendall's problem and limit theorems in high dimensions ⋮ Complete monotonicity involving the divided difference of polygamma functions ⋮ On the monotonicity and convexity of the remainder of the Stirling formula ⋮ Some new quicker continued fraction approximations for the gamma function related to the Nemes' formula ⋮ 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 ⋮ Refinements of Gurland's formula for pi ⋮ Some inequalities for the trigamma function in terms of the digamma function ⋮ A quicker approximation of the gamma function towards the Windschitl's formula by continued fraction ⋮ Monotonicity properties, inequalities and asymptotic expansions associated with the gamma function ⋮ On the asymptotic expansions of the gamma function related to the Nemes, Gosper and Burnside formulas ⋮ New quicker sequences and inequalities with continued fraction towards Euler's constant ⋮ Some new convergent sequences of Glaisher-Kinkelin's and Bendersky-Adamchik's constants ⋮ Some quicker continued fraction approximations and inequalities towards Euler's constant ⋮ A new approximation of the gamma function by expanding the Windschitl's formula ⋮ Continued fractions and inequalities about \(\left( 1+\frac{1}{x}\right)^x\) ⋮ Padé approximant related to asymptotics for the gamma function ⋮ Some new convergent sequences and inequalities of Euler's constant ⋮ Multiple-correction and faster approximation ⋮ A generated approximation related to Gosper's formula and Ramanujan's formula ⋮ Ramanujan's estimate for the gamma function via monotonicity arguments ⋮ New improvements of the Stirling formula ⋮ Some properties of a sequence arising from geometric probability for pairs of hyperplanes intersecting with a convex body ⋮ Some new approximations of Glaisher-Kinkelin's and Bendersky-Adamchik's constants by continued fraction ⋮ A general asymptotic formula of the gamma function based on the Burnside's formula ⋮ New properties of the divided difference of psi and polygamma functions ⋮ Some inequalities involving the polygamma functions ⋮ Completely monotonic degrees for a difference between the logarithmic and psi functions ⋮ The volume of simplices in high-dimensional Poisson-Delaunay tessellations ⋮ Bounds for completely monotonic degrees of remainders in asymptotic expansions of the digamma function
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