A394701 Decimal expansion of the parameter q at the stability limit of the Mathieu equation for the characteristic value 0.

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, 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, 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

Offset

0,1

Comments

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.

Links

Table of n, a(n) for n=0..104.

Eugene I. Butikov, Analytical expressions for stability regions in the Ince-Strutt diagram of Mathieu equation.

Hugo Pfoertner, Stability diagram of the Mathieu equation. The intersection of the right limit curve with the horizontal axis gives the value of q.

Eric Weisstein's World of Mathematics, Mathieu Characteristic Exponent.

Example

0.90804633373457759387058257669953846380028910051159...

Mathematica

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

Crossrefs

Cf. A085550, A176019.

Sequence in context: A248935 A397195 A202955 * A019820 A019985 A242711

Adjacent sequences: A394698 A394699 A394700 * A394702 A394703 A394704

Keyword

nonn,cons

Author

Hugo Pfoertner, Apr 02 2026

Status

approved