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Upper bounds for the first zeros of Bessel functions. (English) Zbl 0616.65017

Upper bounds for the first positive zero of the Bessel functions of first kind \(J_{\mu}(z)\) for \(\mu >-1\) are obtained. Ritz’s approximation method, applied to the eigenvalue problem of a compactself adjoint operator, defined on an abstract separable Hilbert space is used to establish the results.
Reviewer: C.L.Koul

MSC:

65D20 Computation of special functions and constants, construction of tables
65H05 Numerical computation of solutions to single equations
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
65J10 Numerical solutions to equations with linear operators
47A10 Spectrum, resolvent
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References:

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