Ratios of Bessel Functions and Roots of αJν(x) + xJ′ν(x) = 0

Abstract

Derivatives with respect to order ν and argument x of the ratio Jν(x)/Jν+1(x) of Bessel functions are studied for all real values of ν and x. Our results generalize and sharpen previously known results, and allow the deduction of a more complete description, including monotonicity and multiplicity, of the positive roots of the equation αJν(x)+xJ′ν(x)=0 for all real ν and α. © 1999 Academic Press.