

A115365


Decimal expansion of smallest positive root of tan(x) = x.


17



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

1,1


COMMENTS

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 3dimensional 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


REFERENCES

M. Abramowitz, I. A. Stegun, Editors, Handbook of Mathematical Functions, Dover Publications, 1965, Chapter 10.


LINKS

Eric Weisstein's World of Mathematics, Tangent


EXAMPLE

4.4934094579090641753...


MAPLE

Digits:=200; fsolve(x*cos(x)sin(x), x, 4..5);


MATHEMATICA



PROG



CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



