[PDF] Top 20 Inequalities on an extended Bessel function

... of Bessel, modified Bessel, spherical Bessel, and modified spherical Bessel ...the Bessel function of the first kind of order p when b = c = 1, and the modified Bessel ... See full document

... corresponding inequalities of the confluent hypergeometric ...some inequalities of the Turán type for confluent hypergeometric func- tions of the second kind were also ... See full document

... In Figure 1 we report the graphics of the functions Iν t/Iν−1 t solid line and the respective lower bounds fν t short dashed line and gν t long dashed line on the interval 100, 600.. See[r] ... See full document

... Abstract Motivated by the work of Ghoussoub and Moradifam, we prove some improved Hardy inequalities on the Heisenberg group Hn via Bessel function.. Mathematics Subject Classification 2[r] ... See full document

... Schwarz function w, which is analytic in D , with w ( 0 ) = 0, and |w ( z )| < 1 for all z ∈ D , such that f ( z ) = F ( w ( z )) , z ∈ D ...the function F is univalent in D , then we have the following ... See full document

... a function of n and x ...modified Bessel functions, parabolic cylinder functions, Legendre functions of imaginary variable and Laguerre ...Turán-type inequalities are established from the ... See full document

... for all k > 0, calling it the Pochhammer k-symbol. Closely associated functions that have relation with the Pochhammer symbols are the gamma and beta functions. Hence it is use- ful to recall some facts about the ... See full document

... the extended beta ...Turán-type inequalities. The monotonicity, log-convexity, log-concavity of extended hypergeometric functions are deduced by using the inequalities on extended beta ... See full document

... and inequalities for the gamma or incomplete gamma functions are deduced or extended, a unified proof of some known results for the gamma function is ... See full document

... In harmonic analysis the positivity of the translation operator is crucial. It plays a central role in establishing some useful results such as the properties of the convolution product. In contrast to the classical ... See full document

... multiindex Bessel functions, which play a ubiquitous role in wide range of diverse fields such as acoustic field, electromagnetism, heat, hydrodynamics, wave motion, elasticity and optical ...multi-index ... See full document

... As an application of inequality (.), an open problem was proposed, answered and im- proved by Sándor and Bencze in []. Recently, inequality (.) and its related inequalities in [] were extended to ... See full document

... the integral on the right-hand side of (23) converges and can be expressed in terms of the generalized Hurwitz–Lerch zeta function with the help of the integral representation (11) with x = 1. Condition (24) can ... See full document

... Abstract. The article considers the generalized k-Bessel functions and represents it as Wright func- tions. Then we study the monotonicity properties of the ratio of two different orders k- Bessel ... See full document

... Two-sided inequalities for the theory of special functions ap- pear in the literature of many ...two-sided inequalities are motivated by different problems in mathematics, sciences and engineering that ... See full document

... Frequency or phase modulation is an efficient form of communication, where information is transmitted over a carrier signal by changing the instantaneous frequency [4]. Phase modulation has been heavily employed over the ... See full document

... Author details 1 School of Mathematics and Computation Sciences, Hunan City University, Yiyang, 413000, China.. 2 Customer Service Center, State Grid Zhejiang Electric Power Research Ins[r] ... See full document

... give lower and upper bounds for these zeros. The roots of these functions are of interest for several reasons. Firstly, it is intrinsically interesting to provide information about the roots of a function such as ... See full document

... basis function rather than sinusoidals. Bessel functions have damped sinusoidals as basis function, so it is the most effective way for representing speech ...work, bessel features like ... See full document

... The graphs of Bessel functions are similar to the damped sinusoidal solution. In this paper this observation has been investigated by two physical examples. The Bessel’s equation has been compared with the ... See full document