A394701 - OEIS

%I #17 Apr 03 2026 17:56:17

%S 9,0,8,0,4,6,3,3,3,7,3,4,5,7,7,5,9,3,8,7,0,5,8,2,5,7,6,6,9,9,5,3,8,4,

%T 6,3,8,0,0,2,8,9,1,0,0,5,1,1,5,9,6,7,0,9,1,5,1,8,2,2,3,9,0,1,7,2,5,6,

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

%N Decimal expansion of the parameter q at the stability limit of the Mathieu equation for the characteristic value 0.

%C This constant is approximately equal to 3*(sqrt(13)-3)/2 = 1/A176019 = 3*A085550. For a derivation of this relation and a description of the meaning as the limit case of vanishing gravity for principal parametric resonance of a physical pendulum with harmonically moving pivot see Butikov, pages 8-9.

%H Eugene I. Butikov, <a href="http://butikov.faculty.ifmo.ru/Mathieu.pdf">Analytical expressions for stability regions in the Ince-Strutt diagram of Mathieu equation</a>.

%H Hugo Pfoertner, <a href="/A394701/a394701.png">Stability diagram of the Mathieu equation</a>. The intersection of the right limit curve with the horizontal axis gives the value of q.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MathieuCharacteristicExponent.html">Mathieu Characteristic Exponent</a>.

%e 0.90804633373457759387058257669953846380028910051159...

%t RealDigits[q /. FindRoot[MathieuCharacteristicExponent[0, q] == 1, {q, 1}, WorkingPrecision -> 120]][[1]]

%Y Cf. A085550, A176019.

%K nonn,cons

%O 0,1

%A _Hugo Pfoertner_, Apr 02 2026