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MR890269 41A60 (65D30)
Stoyanov, Basil J.; Farrell, Richard A. On the asymptotic evaluation of $\int\sp {\pi/2}\sb 0J\sp 2\sb 0(\lambda\,{\rm sin}\,x)dx$. Math. Comp. 49 (1987), no. 179, 275–279.
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