Laguerre polinomlari

Laguerre polinomlari (Lagger) --- matematik fizikada foydalaniladigan polinomlardan biri hisoblanadi. Edmond Laguerre sharafiga nomlangan. Laguerre differensial tenglamalarining yechimi hisoblanadi. $$xy'' + (1 - x)y' + ny = 0,\ y = y(x)$$ Ushbu tenglama ikkinchi tartibli chiziqli differensial tenglama hisoblanadi. Tenglamaning yechimlari yagona emas. n ta yechimi mavjud.

Ba'zida quyidagi tenglamaning ko`rinishi quyidagi ko`rinishga keltiriladi: $$xy'' + (\alpha + 1 - x)y' + ny = 0~.$$

References

• Andoza:Abramowitz Stegun ref
• G. Szegő, Orthogonal polynomials, 4th edition, Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, RI, 1975.
• Koornwinder, Tom H.; Wong, Roderick S. C.; Koekoek, Roelof; Swarttouw, René F. (2010), „Orthogonal Polynomials“, in Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W. (muh.), NIST Handbook of Mathematical Functions, Cambridge University Press, ISBN 978-0-521-19225-5, MR 2723248.
• B. Spain, M.G. Smith, Functions of mathematical physics, Van Nostrand Reinhold Company, London, 1970. Chapter 10 deals with Laguerre polynomials.
• „Laguerre polynomials“, Encyclopedia of Mathematics, EMS Press, 2001 [1994]
• Eric W. Weisstein, "Laguerre Polynomial", From MathWorld—A Wolfram Web Resource.
• George Arfken and Hans Weber. Mathematical Methods for Physicists. Academic Press, 2000. ISBN 978-0-12-059825-0.