On the zeros of \(J_n(z)\pm iJ_{n+1}(z)\) and \([J_{n+1}(z)]^2- J_n(z) J_{n+2}(z)\). (English) Zbl 0987.65022
The authors proves that the complex zeros of \(J_n(z)\pm iJ_{n+1}(z)\) and \([J_{n+1}(z)]^2-J_n(z)J_{n+2}(z)\) are simple. A software package for calculation zeros is used to illustrate the first 30 zeros.
Reviewer: Matthew He (Ft.Lauderdale)
MSC:
| 65D20 | Computation of special functions and constants, construction of tables |
| 30C15 | Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) |
| 33C10 | Bessel and Airy functions, cylinder functions, \({}_0F_1\) |
| 65H05 | Numerical computation of solutions to single equations |
| 65E05 | General theory of numerical methods in complex analysis (potential theory, etc.) |
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