

A115365


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


15



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


REFERENCES

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


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000
Mohammad K. Azarian, On the Fixed Points of a Function and the Fixed Points of its Composite Functions, International Journal of Pure and Applied Mathematics, Vol. 46, No. 1, 2008, pp. 3744. Mathematical Reviews, MR2433713 (2009c:65129), March 2009. Zentralblatt MATH, Zbl 1160.65015.
Mohammad K. Azarian, Fixed Points of a Quadratic Polynomial, Problem 841, College Mathematics Journal, Vol. 38, No. 1, January 2007, p. 60.
Mohammad K. Azarian, Solution to Fixed Points of a Quadratic Polynomial, Problem 841, College Mathematics Journal Vol. 39, No. 1, January 2008, pp. 6667.
Stanislav Sykora, KSpace Images of nDimensional Spheres and Generalized Sinc Functions
Eric Weisstein's World of Mathematics, Tangent
Eric Weisstein's World of Mathematics, Tanc Function


EXAMPLE

4.4934094579090641753...


MAPLE

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


MATHEMATICA

RealDigits[FindRoot[Tan[x]==x, {x, 4}, WorkingPrecision>128][[1, 2]]][[1]] (* Robert G. Wilson v, Mar 05 2012 *)
RealDigits[BesselJZero[3/2, 1], 10, 100][[1]] (* Vladimir Reshetnikov, May 13 2016 *)


PROG

(PARI) solve(x=4, 4.5, tan(x)x) \\ Charles R Greathouse IV, Jun 10 2012


CROSSREFS

Cf. A102015 (continued fraction), A213053 (amplitude at x).
Cf. A062546, A224196, A207528, A243108, A245333.
Sequence in context: A246668 A021073 A021961 * A263491 A272427 A068340
Adjacent sequences: A115362 A115363 A115364 * A115366 A115367 A115368


KEYWORD

nonn,cons


AUTHOR

Eric W. Weisstein, Jan 21 2006


EXTENSIONS

Mathematica program corrected by Harvey P. Dale, Mar 22 2012


STATUS

approved



