Some properties of Bessel function zeros derived from the wave functions for a particle in an enclosureXXXXXXXXX
(1.2)The differential equation (1.1) permits the study of Bessel and modified Bessel functions all together. It is worth mentioningthat, in particular, when c = 1, we obtain the Bessel function J ν, 1 = J ν , and for c = − 1, the function J ν,− 1 becomes themodified ...
Γ(ν+n+1) (z/2) 2n+ν ,z∈C.(1.2) Thedifferentialequation(1.1)permitsthestudyofBesselandmodifiedBesselfunctionsalltogether.Itisworthmentioning that,inparticular,whenc=1,weobtaintheBesselfunctionJ ν,1 =J ν ,andforc=−1,thefunctionJ ν,−1 becomesthe modifiedBesselfunctionI ν . We...
Monotonicity and Convexity Properties of Zeros of Bessel Functions It is shown that ${{j_{u k} } / u }$ decreases as $u $ increases, $0 kth positive zero of the Bessel function $J_u (x)$. In particular, ${{j_{u 1}^2 } / u ... J.,T.,Lewis,... - 《Siam Journal on...
In this study, we introduce a new class of function called geodesic semi E-b-vex functions and generalized geodesic semi E-b-vex functions and discuss some of their properties. Keywords: Convexity; Geodesic E-convexity; Geodesic E-convex functions; Nonlinear programming; Riemannian manifolds Referen...
Monotonicity and log-convexity properties for the Bessel-Struve kernel, and the ratio of the Bessel-Struve kernel and the Kummer confluent hypergeometric function are investigated. Moreover, lower and upper bounds are given for the Bessel-Struve kernel in terms of the exponential function and some ...
Modified Bessel functionStarlike functionsConvex functionsAnalytic functionsUnivalent functionsClose-to-convex functionsIn this paper, the products of modied Bessel functions of the rst kind are considered. Our main aim is to provide various conditions so that these products have certain geometric ...
Higher monotonicity properties of normalized Bessel functions Denote by Ju03bd the Bessel function of the first kind of order u03bd and u03bcu03bd,k is its kth positive zero. For u03bd > u00bd, a theorem of Lorch, Mul... Liu,Yongping - 《International Journal of Wavelets Multiresolution...
Szego, Monotonicity of the differences of zeros of Bessel functions as a function of order.Proc. Amer. Math. Soc. To appear. E. Makai, On a monotonic property of certain Sturm-Liouville functions.Acta Math. Acad. Sci. Hungar., 3 (1952), 165–172. Article MATH MathSciNet Google Scholar...
We mainly establish a monotonicity property between some special Riemann sums of a convex function f on [a, b], which in particular yields that \\({\\frac{b-a}{n+1} \\sum_{i=0}^n f\\left(a+i\\frac{b-a}{n} ight)}\\) is decreasing while \\({\\frac{b-a}{n-1} \\su...