Laguerre's differential equation xy" + (1-x)y'+ ny = 0, n = 0, 1, 2, ..., has polynomial solutions L(x). Put the equation in self-adjoint form. y]+[ )y=0 Give an orthogonality relation. For m = n, m(x)Ln(x) dx = 0.
Laguerre's differential equation xy" + (1-x)y'+ ny = 0, n = 0, 1, 2, ..., has polynomial solutions L(x). Put the equation in self-adjoint form. y]+[ )y=0 Give an orthogonality relation. For m = n, m(x)Ln(x) dx = 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Laguerre's differential equation
xy" + (1x)y' + ny = 0, n = 0, 1, 2, ...,
has polynomial solutions L,(x). Put the equation in self-adjoint form.
&
y]+[
)y=0
Give an orthogonality relation.
For m # n,
4m(x)L(x) dx = 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff79fcacf-f17e-496c-8bc5-1465285ed933%2Fd8d0219a-b2fb-4923-8591-c0ab1011be02%2Fzuc31d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Laguerre's differential equation
xy" + (1x)y' + ny = 0, n = 0, 1, 2, ...,
has polynomial solutions L,(x). Put the equation in self-adjoint form.
&
y]+[
)y=0
Give an orthogonality relation.
For m # n,
4m(x)L(x) dx = 0.
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