sonia akram
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what is the indicial equation associated with regular singularities x=1 and x=-1 of legendre's eq.?(1-x^2)y''-2xy'+a(a+1)y=0
Indicial Equation for Legendre's Eq. at x=1,-1
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what is the indicial equation associated with regular singularities x=1 and x=-1 of legendre's eq.?(1-x^2)y''-2xy'+a(a+1)y=0
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What have you done to try to find it yourself?
If you write
[tex]y= \sum_{n=0}^\infty a_n x^{n+c}[/itex]<br /> what are y' and y"? What do you get when you put those into the equation?<br /> Assuming a_0 is not 0, what is the coefficient of the lowest power of x in that equation?[/tex]
If you write
[tex]y= \sum_{n=0}^\infty a_n x^{n+c}[/itex]<br /> what are y' and y"? What do you get when you put those into the equation?<br /> Assuming a_0 is not 0, what is the coefficient of the lowest power of x in that equation?[/tex]
matematikawan
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Don't they have a general formula for indicial equation for the Legendre's equation. I remember they have such a formula for Euler-Cauchy differential equation.
sonia akram
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HallsofIvy, that's the series solution for singularity x=0, if we are esprcially working for singularity x=1 or -1 than indicial would be different or not?
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Yes, I was using the most common application as an example. If a differential equation has a singularity at x= x0 you would use
[tex]y= \sum_{n=0}^\infty a_n (x- x_0)^{n+ c}[/tex]
[tex]y= \sum_{n=0}^\infty a_n (x- x_0)^{n+ c}[/tex]
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sonia akram
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thx a lot for ur help!