A series expansion for the first positive zero of the Bessel functions
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- by R. Piessens PDF
- Math. Comp. 42 (1984), 195-197 Request permission
Abstract:
It is shown that the first positive zero ${j_{v,l}}$ of the Bessel function ${J_v}(x)$ is given by \[ {j_{v,l}} = 2{(v + 1)^{1/2}}\left [ {1 + \frac {{(v + 1)}}{4} - \frac {{7{{(v + 1)}^2}}}{{96}} + \frac {{49{{(v + 1)}^3}}}{{1152}} - \frac {{8363{{(v + 1)}^4}}}{{276480}} + \cdots } \right ]\] for $- 1 < v < 0$.References
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Math. Comp. 42 (1984), 195-197
- MSC: Primary 33A40; Secondary 65D20
- DOI: https://doi.org/10.1090/S0025-5718-1984-0725995-7
- MathSciNet review: 725995