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A115365
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Decimal expansion of smallest positive root of tan(x) = x.
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17
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4, 4, 9, 3, 4, 0, 9, 4, 5, 7, 9, 0, 9, 0, 6, 4, 1, 7, 5, 3, 0, 7, 8, 8, 0, 9, 2, 7, 2, 8, 0, 3, 2, 2, 0, 8, 2, 2, 1, 5, 5, 8, 3, 8, 7, 2, 2, 9, 0, 0, 4, 0, 8, 0, 2, 8, 9, 5, 8, 2, 3, 9, 6, 1, 9, 2, 6, 9, 5, 0, 3, 1, 4, 5, 9, 7, 1, 0, 4, 0, 9, 8, 7, 2, 9, 0, 5, 7, 8, 0, 9, 4, 5, 5, 8, 7, 9, 6, 9, 1, 5, 2, 1, 7, 6
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OFFSET
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1,1
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COMMENTS
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Location (for x>0) of the first negative lobe of sinc(x) = sin(x)/x, where sinc(x) attains its absolute minimum of -0.217233628... The function sinc(x) is important in spectral theory (transient data truncation artifacts). - Stanislav Sykora, Mar 05 2012
Also the first root of the sinc(3,x) function, that is, the radial component of the 3D Fourier transform of 3-dimensional unit sphere. Also the first root of the spherical Bessel function of the 1st kind, j_1(x). - Stanislav Sykora, Nov 14 2013
Unique fixed point of the function arctan(x)+Pi, and this fixed point is attractive. - Robert FERREOL, May 09 2023
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REFERENCES
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M. Abramowitz, I. A. Stegun, Editors, Handbook of Mathematical Functions, Dover Publications, 1965, Chapter 10.
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LINKS
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Eric Weisstein's World of Mathematics, Tangent
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EXAMPLE
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4.4934094579090641753...
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MAPLE
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Digits:=200; fsolve(x*cos(x)-sin(x), x, 4..5);
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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