A DIFFERENTIAL INEQUALITY FOR THE POSITIVE ZEROS OF BESSEL-FUNCTIONS

[摘要] It is proved that the positive zeros j(nu,k), k = 1, 2,..., of the Bessel function J(nu)(x) of the first kind and order nu > -1, satisfy the differential inequality j(nu,k) dj(nu,k)/dnu > 1 + (1 + j(nu,k)2)1/2, nu > -1. This inequality improves the well-known inequality dj(nu,k)/dnu > 1, nu > -1, which is the source of a large number of lower and upper bounds for the zeros j(nu,k), k = 1, 2,... .

[发布日期] 1992-12-09

[关键词] DIFFERENTIAL INEQUALITIES;BOUNDS OF ZEROS OF BESSEL FUNCTIONS