On a conjecture regarding the extrema of Bessel functions and its generalization (Q1874432)

For zeros \(j_k\) and \(j_{k+1}\) of any Bessel function with real order and the zeros \(j_k'\) of its derivative, the estimate \(j_k'> \sqrt{j_k j_{k+1}}\) is proved, together with an upper bound for \(j_k'\). The method, using traditional Sturm type arguments based on the normal form of the Bessel equation is quite general, and is lucidly explained.