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Turán type inequalities for modified Bessel functions of the first kind are used to deduce some sharp lower and upper bounds for the asymptotic order parameter of the stochastic Kuramoto model. Moreover, approximation from the Lagrange inversion theorem and a rational approximation are given for the asymptotic order parameter. [ABSTRACT FROM AUTHOR]

Some Turán type inequalities for Struve functions of the first kind are deduced by using various methods developed in the case of Bessel functions of the first and second kind. New formulas, like Mittag–Leffler expansion, infinite product representation for Struve functions of the first kind, are obtained, which may be of independent interest. Moreover, some complete monotonicity results and functional inequalities are deduced for Struve functions of the second kind. These results complement naturally the known results for a particular case of Lommel functions of the first kind, and for modified Struve functions of the first and second kind. [ABSTRACT FROM AUTHOR]

Geometric properties of the Jackson and Hahn–Exton q -Bessel functions are studied. For each of them, three different normalizations are applied in such a way that the resulting functions are analytic in the unit disk of the complex plane. For each of the six functions we determine the radii of starlikeness and convexity precisely by using their Hadamard factorization. These are q -generalizations of some known results for Bessel functions of the first kind. The characterization of entire functions from the Laguerre–Pólya class via hyperbolic polynomials plays an important role in this paper. Moreover, the interlacing property of the zeros of Jackson and Hahn–Exton q -Bessel functions and their derivatives is also useful in the proof of the main results. We also deduce a necessary and sufficient condition for the close-to-convexity of a normalized Jackson q -Bessel function and its derivatives. Some open problems are proposed at the end of the paper. [ABSTRACT FROM AUTHOR]

Turán, Mitrinović–Adamović and Wilker type inequalities are deduced for regular Coulomb wave functions. The proofs are based on a Mittag–Leffler expansion for the regular Coulomb wave function, which may be of independent interest. Moreover, some complete monotonicity results concerning the Coulomb zeta functions and some interlacing properties of the zeros of Coulomb wave functions are given. [ABSTRACT FROM AUTHOR]

In this paper our aim is to present an elementary proof of an identity of Calogero concerning the zeros of Bessel functions of the first kind. Moreover, by using our elementary approach we present a new identity for the zeros of Bessel functions of the first kind, which in particular reduces to some other new identities. We also show that our method can be applied for the zeros of other special functions, like Struve functions of the first kind, and modified Bessel functions of the second kind. [ABSTRACT FROM AUTHOR]

Abstract: Various miscellaneous functional inequalities are deduced for the so-called generalized inverse trigonometric and hyperbolic functions. For instance, functional inequalities for sums, difference and quotient of generalized inverse trigonometric and hyperbolic functions are given, as well as some Grünbaum inequalities with the aid of the classical Bernoulli inequality. Moreover, by means of certain already derived bounds, bilateral bounding inequalities are obtained for the generalized hypergeometric Clausen function. [Copyright &y& Elsevier]

Abstract: Let denote the class of analytic functions defined on the unit disk with the normalization , in and satisfy the condition for all and for some real constants and such that . We find conditions on constants and such that functions in are univalent in . As a consequence of our investigation, we present univalence and starlikeness criteria. As applications, we present conditions such that is in , where denotes the suitably normalized form of the generalized Bessel functions of the first kind. [Copyright &y& Elsevier]

Abstract: In this paper our aim is to deduce some Turán type inequalities for -hypergeometric and -confluent hypergeometric functions. In order to obtain the main results we apply the methods developed in the case of classical Kummer and Gauss hypergeometric functions. [Copyright &y& Elsevier]

Abstract: Complete monotonicity, Laguerre and Turán type inequalities are established for the so-called Krätzel function , defined by where and . Moreover, we prove the complete monotonicity of a determinant function of which entries involve the Krätzel function. [Copyright &y& Elsevier]

Abstract: We present several inequalities for where is the incomplete gamma function. One of our theorems states that the inequalities hold for all nonnegative real numbers if and only if and . Here, denotes the power sum of order t. This extends and complements a result published by Ismail and Laforgia in 2006. [Copyright &y& Elsevier]

Abstract: In this paper our aim is to show that if a probability density function is geometrically concave (convex), then the corresponding cumulative distribution function and the survival function are geometrically concave (convex) too, under some assumptions. The proofs are based on the so-called monotone form of l''Hospital''s rule and permit us to extend our results to the case of the concavity (convexity) with respect to Hölder means. To illustrate the applications of the main results, we discuss in details the geometrical concavity of the probability density function, cumulative distribution function and survival function of some common continuous univariate distributions. Moreover, at the end of the paper, we present a simple alternative proof to Schweizer''s problem related to the Mulholland''s generalization of Minkowski''s inequality. [Copyright &y& Elsevier]

Abstract: In this paper we study the generalized Marcum Q-function of order real, defined by where , and stands for the modified Bessel function of the first kind. Our aim is to improve and extend some recent results of Wang to the generalized Marcum Q-function in order to deduce some sharp lower and upper bounds. In both cases and we give the best possible upper bound for . The key tools in our proofs are some monotonicity properties of certain functions involving the modified Bessel function of the first kind. These monotonicity properties are deduced from some results on modified Bessel functions, which have been used in wave mechanics and finite elasticity. [Copyright &y& Elsevier]

Abstract: In this paper we consider the probability density function (pdf) of a non-central distribution with arbitrary number of degrees of freedom. For this function we prove that can be represented as a finite sum and we deduce a partial derivative formula. Moreover, we show that the pdf is log-concave when the degrees of freedom is greater or equal than 2. At the end of this paper we present some Turán-type inequalities for this function and an elegant application of the monotone form of l''Hospital''s rule in probability theory is given. [Copyright &y& Elsevier]

Abstract: In this paper we study the monotonicity properties of some functions involving the Mills'' ratio of the standard normal law. From these we deduce some new functional inequalities involving the Mills'' ratio, and we show that the Mills'' ratio is strictly completely monotonic. At the end of this paper we present some Turán-type inequalities for Mills'' ratio. [Copyright &y& Elsevier]

Abstract: The intrinsic properties, including logarithmic convexity (concavity), of the modified Bessel functions of the first kind and some other related functions are obtained. Several inequalities involving functions under discussion are established. [Copyright &y& Elsevier]

Abstract: This paper is motivated by an open problem of Anderson, Vamanamurthy, and Vuorinen. We prove a chain of inequalities for hypergeometric functions, generalized and normalized Bessel functions, Kummer functions and for some general power series. Some particular cases and refinements are given. [Copyright &y& Elsevier]

Abstract: Let be the generalized and normalized Bessel function depending on parameters and let , . Motivated by an open problem of Anderson, Vamanamurthy, and Vuorinen we prove that for all for certain conditions on the parameters . [Copyright &y& Elsevier]

The asymptotic behaviour, with respect to the large order, of the radii of starlikeness of two types of normalised Bessel functions is considered. We derive complete asymptotic expansions for the radii of starlikeness and provide recurrence relations for the coefficients of these expansions. The proofs rely on the notion of Rayleigh sums and asymptotic inversion. The techniques employed in the paper could be useful to treat similar problems where inversion of asymptotic expansions is involved. [ABSTRACT FROM AUTHOR]