On the zeros and turning points of special functions

Globally convergent fixed point iterations, together with bounds on differences of zeros from Sturm methods, are used to build efficient algorithms for the computation of the zeros of special functions satisfying first-order linear difference–differential equations. Bounds on the spacing between the zeros are obtained as a by-product. Turning points can also be computed in a similar way; new analytical information is also obtained in this case which, for instance, can be used to prove a conjecture by Elbert on the turning points of Bessel functions.