“Laguerre Differential Equation”的概念、定义、习题解题方法及翻译-数学辞典

单词

Laguerre Differential Equation

释义

Laguerre Differential Equation

(1)

The Laguerre differential equation is a special case of the more general ``associated Laguerre differential equation''

(2)

with

. Note that if

, then the solution to the associated Laguerre differential equation is of theform

(3)

and the solution can be found using an Integrating Factor


			(4)

(5)

The associated Laguerre differential equation has a Regular Singular Point at 0 and an IrregularSingularity at . It can be solved using a series expansion,


	(6)


	(7)


	(8)

(9)

(10)

This requires

			(11)
			(12)

for

. Therefore,

(13)

for

, 2, ..., so

(14)

is a Positive Integer, then the series terminates and the solution is a Polynomial, knownas an associated Laguerre Polynomial (or, if

, simply aLaguerre Polynomial).

See also Laguerre Polynomial

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