## Mathieu Function

The form given by Whittaker and Watson (1990, p. 405) defines the Mathieu function based on the equation

 (1)

This equation is closely related to Hill's Differential Equation. For an Even Mathieu function,
 (2)

where . For an Odd Mathieu function,
 (3)

Both Even and Odd functions satisfy
 (4)

Letting transforms the Mathieu Differential Equation to
 (5)

See also Mathieu Differential Equation

References

Abramowitz, M. and Stegun, C. A. (Eds.). Mathieu Functions.'' Ch. 20 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 721-746, 1972.

Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 562-568 and 633-642, 1953.

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

© 1996-9 Eric W. Weisstein
1999-05-26