MathieuCharacteristicB[r, q] gives the characteristic value for odd Mathieu functions with characteristic exponent r and parameter q.
Mathematical function (see Section A.3.10).
The characteristic value gives the value of the parameter in for which the solution has the form where is an odd function of with period .
When is not a real integer, MathieuCharacteristicB gives the same results as MathieuCharacteristicA.
See notes for MathieuCharacteristicA.
See The Mathematica Book: Section 3.2.12.