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## #1 Help Me ! » Eigenvalue problem not Sturm Liouville » 2014-04-16 01:35:58

mathmari
Replies: 0

Hey!!!

Knowing that:
"The eigenvalue problem  Ly=(py')'+qy, a <= x <= b is a Sturm-Liouville problem when it satisfies the boundary conditions:

,where
is the wronskian."

I have to show that the eigenvalue problem y''+λy=0, with boundary conditions y(0)=0, y'(0)=y'(1) is not a Sturm -Liouville problem.

This is what I've done so far:

Let

solutions of the eigenvalue problem y''+λy=0 , then:
u(0)=0, u'(0)=u'(1) and   v^*(0)=0, v^{*'}(0)=v^{*'}(1).

W(u(0),v^*(0))=u(0)v^{*'}(0)-u'(0)v^*(0)=0

W(u(1),v^*(1))=u(1)v^{*'}(1)-u'(1)v^*(1)=u(1) v^{*'}(0)-u'(0)v^*(1)

How can I continue? How can I show that this is not equal to

?

## #2 Help Me ! » Stirling's formula » 2013-03-31 08:09:03

mathmari
Replies: 1

Hello!!! Could anyone help me to solve this exercise?

Using Stirling's formula show that( see the first uploaded image), where S(x)=-xlnx-(1-x)ln(1-x), 0<=x<=1.
I used n!=e^(-n)n^(n+1/2)(2π)^(1/2)*(1+O(1/n)) and my result is (see the second uploaded image).
Is this equal to the result i have to show??

Thank you!!!!