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[SOLVED] Another Frobenius method ODE

ognik

Active member
Feb 3, 2015
471
Frobenius method - recurrance relation question

If, using the Frobenius method, I get a 3 term recurrence relation of the form $a_{j+2} = a_j .f(k,j) + a_{j-2}. g(k,j)$ ( j even), how do I treat the $a_{j-2}$ term at first? I have found $a_1 = 0$, but how do I find a value for $a_{-2}$ so as to start the recurrance?

Addendum: I found a solution to this but it just says $a_{-2} = 0 = a_{-4}$ by definition. This is very unsatisfying, I use the indicial eqtn to find $a_1$ - but just assume $a_{-2} = 0$ 'by definition? Can anyone shed any more light on this please?
 
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