Laguerre polinomlari

Laguerre polinomlari (Lagger) --- matematik fizikada foydalaniladigan polinomlardan biri hisoblanadi. Edmond Laguerre sharafiga nomlangan. Laguerre differensial tenglamalarining yechimi hisoblanadi. $$x{y}^{″}+(1-x)y^{\prime }+ny=0,y=y(x)$$ Ushbu tenglama ikkinchi tartibli chiziqli differensial tenglama hisoblanadi. Tenglamaning yechimlari yagona emas. Andoza:Mvar ta yechimi mavjud.

Ba'zida quyidagi tenglamaning ko`rinishi quyidagi ko`rinishga keltiriladi: $$x{y}^{″}+(\alpha +1-x)y^{\prime }+ny=0.$$

References

• Andoza:Abramowitz Stegun ref
• G. Szegő, Orthogonal polynomials, 4th edition, Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, RI, 1975.
• Andoza:Dlmf
• B. Spain, M.G. Smith, Functions of mathematical physics, Van Nostrand Reinhold Company, London, 1970. Chapter 10 deals with Laguerre polynomials.
• Andoza:Springer
• Eric W. Weisstein, "Laguerre Polynomial", From MathWorld—A Wolfram Web Resource.
• Andoza:Cite book