In mathematics, the spheroidal wave equation is given by
It is a generalization of the Mathieu differential equation.see Abramowitz and Stegun, page 722 If is a solution to this equation and we define , then is a prolate spheroidal wave function in the sense that it satisfies the equationsee Bateman, page 442
See also Wave equation
References
Bibliography M. Abramowitz and I. Stegun, Handbook of Mathematical function (US Gov. Printing Office, Washington DC, 1964) H. Bateman, Partial Differential Equations of Mathematical Physics (Dover Publications, New York, 1944)