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Estimations of psi function and harmonic numbers
Applied Mathematics and Computation, 2015The asymptotic expansion of digamma function is a starting point for the derivation of approximants for harmonic sums or Euler-Mascheroni constant. It is usual to derive such approximations as values of logarithmic function, which leads to the expansion of the exponentials of digamma function.
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Continued Fractions for the PSI Function and Its Derivatives
SIAM Journal on Applied Mathematics, 1971It is shown that the series part of higher derivatives of the logarithm of the gamma function can be expressed as a Stieltjes transform. This leads to continued fraction developments of Stieltjes type and J-fraction form. The first few terms in the fractions are given for some of the lower derivatives, and a few partial quotients are derived in the ...
Shenton, L. R., Bowman, K. O.
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On the computation of Tricomi's ψ function
Computing, 1974Two methods for calculating Tricomi's confluent hypergeometric function are discussed. Both methods are based on recurrence relations. The first method converges like $$\exp ( - \alpha |\lambda |^{1/3} n^{2/3} )for some \alpha > 0$$ and the second like
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Some properties of functions related to the gamma and psi functions
Integral Transforms and Special Functions, 2010In this paper, several properties associated with the complete monotonicity, the strongly complete monotonicity and the logarithmically complete monotonicity of functions related to the gamma and psi functions are obtained. Relevant connections of the results presented here with those derived in earlier works are also pointed out.
Chao-Ping Chen +2 more
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Bounds and Completely Monotonicity of Some Functions Involving the Functions ψ′(l) and ψ″(l)
2022Symmetrical patterns exist in the nature of inequalities, which play a basic role in theoretical and applied mathematics. In several studies, inequalities present accurate approximations of functions based on their symmetry properties. In the paper, we prove the completely monotonic (CM) property of some functions involving the function Δ(l)=ψ
Omelsaad Ahfaf +2 more
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TWO NEW PROOFS OF THE COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE PSI FUNCTION
Bulletin of the Korean Mathematical Society, 2010Bai-Ni Guo, Feng Qi
exaly
Sharp inequalities for the psi function and harmonic numbers
Analysis (Germany), 2014Bai-Ni Guo, Feng Qi
exaly