It arises in separation of variables of Laplace's Equation in Elliptic Cylindrical Coordinates. Whittaker and Watson (1990) use a slightly different form to define the Mathieu Functions.

The modified Mathieu differential equation

arises in Separation of Variables of the Helmholtz Differential Equation in Elliptic Cylindrical Coordinates.

**References**

Abramowitz, M. and Stegun, C. A. (Eds.).
*Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.*
New York: Dover, p. 722, 1972.

Morse, P. M. and Feshbach, H. *Methods of Theoretical Physics, Part I.* New York: McGraw-Hill, pp. 556-557, 1953.

Whittaker, E. T. and Watson, G. N. *A Course in Modern Analysis, 4th ed.* Cambridge, England:
Cambridge University Press, 1990.

© 1996-9

1999-05-26