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J1(Z)

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Originally appearing in Volume V08, Page 242 of the 1911 Encyclopedia Britannica.
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J1(Z) _2 - 22.4+22.42.6 22.42.62.8 + . When z is See also:great, we may employ the semi-convergent See also:series , ~/ See also:r2 1 3 1 _3.5.7.1.3 3.5.7.9.11.1.3.5. I-'V .`zr) co*—170 8 z 8.16.24 (i) + 8.16.24.32.40 7 \i) s— • (10). A table of the values of 2z-'Jl(z) has been given by E. C. J. Lommel (Schlomilch, 187o, 15, p. 166), to whom is due the first systematic application of See also:Bessel's functions to the diffraction integrals. The See also:illumination vanishes in See also:correspondence with the roots of the See also:equation Jl(z) =o. If these be called z2, z3, ... the radii of the dark rings in the diffraction See also:pattern are 'zi f1z2 2xR ' See also:ark' ' ' being thus inversely proportional to R. The integrations may also be effected by means of polar co-ordinates, taking first the integration with respect to r"so as to obtain the result for an infinitely thin See also:annular See also:aperture. Thus, if x=p See also:cos y=p See also:sin (p, C = ff cos px dx dy = f R f02 r cos (pp cos 0) pdp do.

End of Article: J1(Z)

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