Accurate Estimates of the Gamma Function Involving the PSI Function

Abstract

The main result of this article is to establish new and accurate approximations of the gamma function in terms of the digamma function, that improve a result of Alzer and Batir [Appl. Math. Lett. 20(2007):778-781].

The monotonicity and convexity of a function involving digamma one and their applications

“…which converges to γ as n −3 proved by Motici in [31]. In a very recent papers [26], [27], [31], [32], [34], [33], [28], [30], C. Mortici established serval new sequences converge to γ at faster rate, for instance, he [30] proved that the sequences (u n ) and (v n ) defined by, respectively,…”

“…A detailed list of references is given in [26]. In addition, some new results can be found in [6], [7], [8], [9], [11], [12], [13], [14], [15], [16], [19], [17], [18], [20], [23], [25], [27], [34], [36], [37], [39], and closely-related references therein.…”

Inequalities involving the gamma and digamma functions

“…In 2011 C. Mortici [11] improved the upper and lower bounds given in (1.4) and proved the following inequalities for x ≥ 2:…”

An approximation formula for n!

“…The problem of approximating the gamma function, in particular, the factorial function has been attracted the attention of many mathematicians recently, and a lot of paper concerning this problem have been published; see for example [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. The most well known approximation formula for n!…”