

A244350


Decimal expansion of 'lambda', a Sobolev isoperimetric constant related to the "rod inequality", arising from the elasticity study of a rod that is clamped at both ends.


0



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

1,1


REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.6 Sobolev Isoperimetric Constants, p. 221.


LINKS

Table of n, a(n) for n=1..103.


FORMULA

lambda = theta^4/Pi^4 = 1/(Pi^4*mu), where theta is A076414 and mu is A244347.
lambda is also the smallest eigenvalue of the ODE g''''(x)=lambda*g(x), g(0)=g'(0)=g(Pi)=g'(Pi)=0.


EXAMPLE

5.13878013260283423689422...


MATHEMATICA

digits = 103; theta = x /. FindRoot[Cos[x]*Cosh[x] == 1, {x, 5}, WorkingPrecision > digits+10]; lambda = theta^4/Pi^4; RealDigits[lambda, 10, digits] // First


CROSSREFS

Cf. A076414 (theta), A244347 (mu).
Sequence in context: A214803 A225984 A074048 * A176321 A248130 A134894
Adjacent sequences: A244347 A244348 A244349 * A244351 A244352 A244353


KEYWORD

nonn,cons,easy


AUTHOR

JeanFrançois Alcover, Jun 26 2014


STATUS

approved



