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Numerical algorithms for the real zeros of hypergeometric functions
Algorithms for the computation of the real zeros of hypergeometric functions
which are solutions of second order ODEs are described. The algorithms are
based on global fixed point iterations which apply to families of functions
satisfying first order linear difference differential equations with continuous
coefficients. In order to compute the zeros of arbitrary solutions of the
hypergeometric equations, we have at our disposal several different sets of
difference differential equations (DDE). We analyze the behavior of these
different sets regarding the rate of convergence of the associated fixed point
iteration. It is shown how combinations of different sets of DDEs, depending on
the range of parameters and the dependent variable, is able to produce
efficient methods for the computation of zeros with a fairly uniform
convergence rate for each zero.Comment: 21 pages, 6 Figure