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A series expansion for the first positive zero of the Bessel functions

Author: R. Piessens
Journal: Math. Comp. 42 (1984), 195-197
MSC: Primary 33A40; Secondary 65D20
MathSciNet review: 725995
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Abstract: It is shown that the first positive zero $ {j_{v,l}}$ of the Bessel function $ {J_v}(x)$ is given by

$\displaystyle {j_{v,l}} = 2{(v + 1)^{1/2}}\left[ {1 + \frac{{(v + 1)}}{4} - \fr... ...(v + 1)}^3}}}{{1152}} - \frac{{8363{{(v + 1)}^4}}}{{276480}} + \cdots } \right]$

for $ - 1 < v < 0$.

References [Enhancements On Off] (What's this?)

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Article copyright: © Copyright 1984 American Mathematical Society