6533b857fe1ef96bd12b3c8d

RESEARCH PRODUCT

Further monotonicity and convexity properties of the zeros of cylinder functions

Lucia G. RodonoCarla Giordano

subject

CerobiologyApplied MathematicsMathematical analysisRegular polygonZero (complex analysis)Monotonic functionFunction (mathematics)biology.organism_classificationConvexityCombinatoricsComputational Mathematicssymbols.namesakeZeros of Bessel functionssymbolsConvex functionBessel functionMathematics

description

AbstractLet cvk be the kth positive zero of the cylinder function Cv(x,α)=Jv(x) cos α−Yv sin α, 0⩽α<π, where Jv(x) and Yv(x) are the Bessel functions of the first and the second kind, respectively. We prove that the function v(d2cvkddv2+δ)cvk increases with v⩾0 for suitable values of δ and k−απ⩾ 0.7070… . From this result under the same conditions we deduce, among other things, that cvk+12δv2 is convex as a function of v⩾0. Moreover, we show some monotonicity properties of the function c2vkv. Our results improve known results.

yearjournalcountryeditionlanguage
1992-10-01Journal of Computational and Applied Mathematics
https://doi.org/10.1016/0377-0427(92)90078-c