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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), , stating this convexity for ν > 0. Also the monotonicity properties of thedoi:10.4153/cmb-1999-007-4 fatcat:nkxlyp4u7ndwbeqoy6ab7gzq7i