Ince equation

In mathematics, the Ince equation, named for Edward Lindsay Ince, is the differential equation

$w^{\prime \prime }+\xi \sin (2z)w^{\prime }+(\eta -p\xi \cos (2z))w=0.$

When p is a non-negative integer, it has polynomial solutions called Ince polynomials.

See also

• Whittaker–Hill equation
• Ince–Gaussian beam

References

• Boyer, Charles P.; Kalnins, E. G.; Jr., W. (1975), "Lie theory and separation of variables. VII. The harmonic oscillator in elliptic coordinates and Ince polynomials" (PDF), Journal of Mathematical Physics, 16: 512–517, Bibcode:1975JMP....16..512B, doi:10.1063/1.522574, ISSN 0022-2488, MR 0372384
• Magnus, Wilhelm; Winkler, Stanley (1966), Hill's equation, Interscience Tracts in Pure and Applied Mathematics, No. 20, Interscience Publishers John Wiley & Sons\, New York-London-Sydney, ISBN 978-0-486-49565-1, MR 0197830
• Mennicken, Reinhard (1968), "On Ince's equation", Archive for Rational Mechanics and Analysis, Springer Berlin / Heidelberg, 29: 144–160, Bibcode:1968ArRMA..29..144M, doi:10.1007/BF00281363, ISSN 0003-9527, MR 0223636
• Wolf, G. (2010), "Equations of Whittaker–Hill and Ince", in Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W. (eds.), NIST Handbook of Mathematical Functions, Cambridge University Press, ISBN 978-0-521-19225-5, MR 2723248