[PDF] Top 20 On rational bounds for the gamma function

... 4 Results and discussion In this paper, we provide the accurate bounds for the classical gamma function in terms of very simple rational functions, which can be used to estimate the valu[r] ... See full document

... As mentioned in Remark 3.6, the double inequality 3.6 and its sharpness were recovered and proved once and again in some papers such as 70, 86–92, 172–174 and 108, Theorem 2 , because of either without being aware of and ... See full document

... As a consequence, we get some new sharp estimates to various classical inequalities concerning the gamma function and hyperbolic functions.... Acknowledgements This paper is supported by[r] ... See full document

... variance gamma process (Avramidis, L’Ecuyer, and Tremblay ...two gamma processes at any finite set of times containing 0 and T , we can compute bounds on the VG path everywhere on (0, T ... See full document

... [17] F. Qi, A class of logarithmically completely monotonic functions and application to the best bounds in the second Gautschi-Kershaw’s inequality, Comput. Math. Appl. (2006), accepted. RGMIA Res. Rep. Coll. 9 ... See full document

... the gamma function, and prove that those functions, involving the gamma function and Windschitl type functions, have good properties, including monotonicity and ...type bounds for the ... See full document

... 4. Barnes, EW: The genesis of the double gamma functions. Proc. Lond. Math. Soc. S1-31(1), 358-381 (1900) 5. Barnes, EW: The theory of the double gamma function. Philos. Trans. R. Soc. Lond. Ser. A ... See full document

... Remark 2.5.3. Any one of the bounds in (2.28) may be derived from the other one by Boyd’s method in [21] (see Section 3.4), by Shanbhag’s technique in [153] (see Section 3.5), by Raja Rao’s technique in [142] (see ... See full document

... [13] F. Qi, B.-N. Guo, and Ch.-P. Chen, Some completely monotonic functions involving the gamma and polygamma functions, J. Austral. Math. Soc. 80 (2006), 81–88. RGMIA Res. Rep. Coll. 7 (2004), no. 1, Art. 5, ... See full document

... In 2005 the papers [4, 22] gave two alternative proofs for Theorem 1 respec- tively by using the convolution theorem of Laplace transforms, some asymptotic formulas and integral representations of the gamma ... See full document

... the gamma and psi functions have many applications in the areas of mathematics, physics, and engineering ...the bounds for the gamma and psi functions have attracted the interest of many ...psi ... See full document

... In this paper, we present the monotonicity and absolute monotonicity properties for the two-parameter hyperbolic and trigonometric functions. As applications, we find several complete monotonicity properties for the ... See full document

... 53. Nemes, G: More accurate approximations for the gamma function. Thai J. Math. 9, 21-28 (2011) 54. Nemes, G: New asymptotic expansion for the Gamma function. Arch. Math. (Basel) 95, 161-169 ... See full document

... in rational normal scrolls, which may be viewed as the join of two rational normal curves lying in hy- perplanes of complementary ...and bounds for the number of total and ordinary ramification points ... See full document

... BOUNDS FOR THE MEAN SQUARE ERROR OF RELIABILITY ESTIMATION FROM GAMMA DISTRIBUTION IN PRESENCE OF AN OUTLIER OBSERVATION M.E.. GHITANY and W.H.[r] ... See full document

... the function Γ(x + λ)/Γ(x + 1) and the gamma function Γ(x) with usual notation, where x > 0 and 0 < λ < 1 is independent of x, have been studied by many authors, ... See full document

... the function g, the generalized k-fractional integral operator of f on [a, b], the generalized Hadamard k- fractional integral operator of f , and the generalized (k, s)-fractional integral operator of f on [a, ... See full document

... In this paper, two classes of functions, involving a parameter and the Euler gamma function, and two functions, involving the Euler gamma function, are verified to be logarithmically com[r] ... See full document

... Using the Alzer integral inequality and the elementary properties of the gamma function, a double inequality for gamma function is established, which is an improvement of Merkle’s inequality. ... See full document

... Remark 3 In this paper, we investigate the monotonicity of the function f (x). In general, it is difficult to deal with such monotonicity since the gamma function occurs in denom- inator. However, by ... See full document