A series expansion for the first positive zero of the Bessel functions
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 Math. Comp. 42 (1984), 195197 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), 195197
 MSC: Primary 33A40; Secondary 65D20
 DOI: https://doi.org/10.1090/S00255718198407259957
 MathSciNet review: 725995