On the Square of the First Zero of the Bessel Function $J_\nu(z)$

Árpád Elbert, Panayiotis D. Siafarikas
1999 Canadian mathematical bulletin  
Let j ν,1 be the smallest (first) positive zero of the Bessel function J ν (z), ν > −1, which becomes zero when ν approaches −1. Then j 2 ν,1 can be continued analytically to −2 < ν < −1, where it takes on negative values. We show that j 2 ν,1 is a convex function of ν in the interval −2 < ν ≤ 0, as an addition to an old result [Á. Elbert and A. Laforgia, SIAM J. Math. Anal. 15(1984), [206][207][208][209][210][211][212], stating this convexity for ν > 0. Also the monotonicity properties of the
more » ... properties of the functions
doi:10.4153/cmb-1999-007-4 fatcat:nkxlyp4u7ndwbeqoy6ab7gzq7i