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Computing zeros and orders of Bessel functions. (English) Zbl 0758.65011
This paper contains the development of an algorithm and convergence analysis that is needed for the construction of software for finding zeros of Bessel functions $J\sb m(x)$. The authors consider computing a prescribed number of smallest positive zeros of Bessel functions and of their derivatives of a prescribed order within a prescribed relative error. They also discuss the inverse problems for finding the order of the Bessel function that has a zero of a prescribed order at a prescribed positive value.

65D20Computation of special functions, construction of tables
65H05Single nonlinear equations (numerical methods)
33C10Bessel and Airy functions, cylinder functions, ${}_0F_1$
Full Text: DOI
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