Browsing by Author "Batir, Necdet"

Now showing 1 - 8 of 8

Inequalities for the Double Gamma Function
(Academic Press inc Elsevier Science, 2009) Batir, Necdet
We establish various new upper and lower bounds in terms of the classical gamma and digamma functions for the double gamma function (or Barnes G-function). (c) 2008 Elsevier Inc. All rights reserved.
On Some Properties of the Gamma Function
(Elsevier Gmbh, Urban & Fischer verlag, 2008) Batir, Necdet
In this paper we prove a complete monotonicity theorem and establish some upper and lower bounds for the gamma function in terms of digamma and polygamma functions. (C) 2007 Elsevier GmbH. All rights reserved.
Monotonicity Properties of the Gamma Function
(Pergamon-elsevier Science Ltd, 2007) Alzer, Horst; Batir, Necdet
Let Gc(x) = log Gamma(x) - x log x + x- 1/2log(2 pi) + 1/2 psi(x + c) (x > 0; c >= 0). We prove that G(a) is completely momotonic on (0, infinity) if and only a >= 1/3. Also, -G(b) is completely monotonic on (0, infinity) if and only if b = 0. An application of this result reveals that the best possible nonnegative constants alpha, beta in root 2 pi x(x) exp (-x - 1/2 psi(x + alpha) < Gamma (x) < root 2 pi x(x) exp (-x - 1/2 psi(x + beta) (x > 0) are given by alpha = 1/3 and beta + 0. (c) 2006 Elsevier Ltd. All rights reserved.
On Some Properties of Digamma and Polygamma Functions
(Academic Press inc Elsevier Science, 2007) Batir, Necdet
In this note we present some new and structural inequalities for digamma, polygamma and inverse polygamma functions. We also extend, generalize and refine some known inequalities for these important functions. (c) 2006 Elsevier Inc. All rights reserved.
Sharp Inequalities Involving the Constant E and the Sequence (1
(Taylor & Francis Ltd, 2009) Batir, Necdet; Cancan, Murat
Several new and sharp inequalities involving the constant e and the sequence (1 + 1/n)(n) are proved.
New Inequalities for the Hurwitz Zeta Function
(indian Acad Sciences, 2008) Batir, Necdet
We establish various new inequalities for the Hurwitz zeta function. Our results generalize some known results for the polygamma functions to the Hurwitz zeta function.
Very Accurate Approximations for the Factorial Function
(Element, 2010) Batir, Necdet
We establish the following new Stirling-type approximation formulas for the factorial function n! approximate to root 2 pi n(n)e(-n) root n + 1/6 + 1/72n - 31/6480n(2) - 139/155520n(3) + 9871/6531840n(4) and n! approximate to root 2 pi n(n)e(-n) (4)root n(2) vertical bar n/3 vertical bar 1/18 2/405n 31/9270n(2). Our estimations give much more accurate values for the factorial function than some previously published strong formulas. We also derive new sequences converging to Euler-Mascheroni constant gamma very quickly.
Inequalities for the Gamma Function
(Springer Basel Ag, 2008) Batir, Necdet
Some inequalities for the gamma function are given. These results refine the classical Stirling approximation and its many recent improvements.