Monotonicity Properties of Determinants of Special Functions

A note on Turán type and mean inequalities for the Kummer function

“…In this case, inequality (11) completes the results of M.E.H. Ismail and A. Laforgia [11] and of Á. Baricz [3,5] regarding the Gaussian hypergeometric function 2 F 1 . See for example Theorems 2.13 and 2.14 in [11] and Theorem 2.17 in [3].…”

“…See for example Theorems 2.13 and 2.14 in [11] and Theorem 2.17 in [3]. The first inequality in (11) follows as in Theorem 1. The second inequality in (11) follows by using a generalized version of (5) (see [14,Identity 30,p.…”

“…Ismail and A. Laforgia [11] and of Á. Baricz [3,5] regarding the Gaussian hypergeometric function 2 F 1 . See for example Theorems 2.13 and 2.14 in [11] and Theorem 2.17 in [3]. The first inequality in (11) follows as in Theorem 1.…”

“…Inequalities involving contiguous Kummer confluent hypergeometric functions of the form Φ(a ± ν, c ± ν, x) and Φ(a, c ± ν, x) were presented in Theorem 2 of [4] and Theorem 2.7 of [11]. These inequalities are of the Turán type [15] in the case that ν = 1.…”

Monotonicity and convexity of the ratios of the first kind modified Bessel functions and applications

“…For various recurrence formulas and many important properties of modified Bessel functions, readers can refer to the classical book of Watson [41]. In recent decades, Turán type inequalities for special functions including the modified Bessel functions have attracted the attention of many mathematicians (see, for example, [26,20,6,3,8,9,25,13]). In fact, Turán type inequalities for the modified Bessel functions and related results appeared in many problems of probability and statistics [19,34,16], chemistry [28], physics [40,38] and engineering sciences [24].…”