A242402 Decimal expansion of the smallest positive root of the equation J_0(t)*I_1(t)+I_0(t)*J_1(t) = 0 (with I_0, I_1, J_0 and J_1, Bessel functions).

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

Offset: 1

Author

Jean-François Alcover, May 13 2014

Keywords

• nonn
• cons

Comments

"This [constant] is associated with the study of a vibrating, homogeneous plate clamped at the boundary [of the unit disk]." - Quoted from Steven R. Finch.

Examples

			3.196220616582541093980527403403720341599...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 222.

Crossrefs

Cf. A115368.

Programs

Mathematica

FindRoot[BesselJ[0, t]*BesselI[1, t] + BesselI[0, t]*BesselJ[1, t] == 0, {t, 3}, WorkingPrecision -> 100][[1, 2]] // RealDigits[#, 10, 100]& // First

PARI

solve(t=3,4, besselj(0,t)*besseli(1,t)+besseli(0,t)*besselj(1,t)) \\ Charles R Greathouse IV, Oct 23 2023