Bounds for the first positive zero of a mixed Bessel function

The present article is concerned with lower and upper bounds of the first positive zero of the function H_ν(z, α) = αJ_ν(z) + zJ′_ν(z), Where J_gn(z) is the ordinary Bessel function of order ν > −1 and J′_ν(z) is the derivative of J_ν(z). A lower bound found here improves and extends the range of validity of the order ν, of a lower bound found in a previous work 8]. Also, two upper bounds given here improve a previously known upper bound 8]. In the particular case α = 0, these bounds lead to lower and upper bounds for the first positive zero j′_ν,1 of J′_ν(z) which improve well-known bounds in the literature.