

A115368


Decimal expansion of first zero of the Bessel function J_0(z).


19



2, 4, 0, 4, 8, 2, 5, 5, 5, 7, 6, 9, 5, 7, 7, 2, 7, 6, 8, 6, 2, 1, 6, 3, 1, 8, 7, 9, 3, 2, 6, 4, 5, 4, 6, 4, 3, 1, 2, 4, 2, 4, 4, 9, 0, 9, 1, 4, 5, 9, 6, 7, 1, 3, 5, 7, 0, 6, 9, 9, 9, 0, 9, 0, 5, 9, 6, 7, 6, 5, 8, 3, 8, 6, 7, 7, 1, 9, 4, 0, 2, 9, 2, 0, 4, 4, 3, 6, 3, 4, 3, 7, 6, 0, 1, 4, 5, 2, 5, 4, 7, 8, 6, 8, 9
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OFFSET

1,1


COMMENTS

"This [constant] arises from the study of a vibrating, homogeneous membrane that is uniformly stretched across the unit disk. [Its square] is the principal frequency of the sound one hears when a kettledrum is struck."  Quoted from the book by Steven R. Finch.
Siegel proves (the Main Theorem) that J_0(z) is transcendental if z is algebraic and nonzero, but since in our case J_0(z) = 0 is not transcendental it follows that z cannot be algebraic.  Charles R Greathouse IV, Oct 20 2020


REFERENCES

Chi Keung Cheung et al., Getting Started with Mathematica, 2nd Ed. New York: J. Wiley (2005) p. 7.
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 221.
C. Siegel, Über einige Anwendungen Diophantischer Approximationen, Abh. Preuss. Akad. Wiss. 1929/30, No. 1. Translated as "On some applications
of Diophantine approximations" by Clemens Fuchs.


LINKS

Table of n, a(n) for n=1..105.
Eric Weisstein's World of Mathematics, Bessel Function Zeros
Index entries for transcendental numbers


EXAMPLE

2.4048255576957727686...


MATHEMATICA

RealDigits[BesselJZero[0, 1], 10, 120][[1]] (* Alonso del Arte, May 06 2011 *)


PROG

(PARI) solve(x=2, 3, besselj(0, x)) \\ Charles R Greathouse IV, Feb 19 2014


CROSSREFS

Cf. A115369, A115370, A115371, A115372, A115373.
Cf. A000275, A002190, A188489, A181167, A181168.
Sequence in context: A152648 A327898 A140875 * A086932 A331762 A221255
Adjacent sequences: A115365 A115366 A115367 * A115369 A115370 A115371


KEYWORD

nonn,cons


AUTHOR

Eric W. Weisstein, Jan 21 2006


STATUS

approved



