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Math Help - 3rd Order Recurrence Relation

  1. #1
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    3rd Order Recurrence Relation

    Hi,

    I have a 3rd Order Homogenous Recurrence Relation, with a characteristic polynomial of

    x^3 - r1x^2 - r2x - r3. This polynomial has three roots, \lambda1, \lambda2, \lambda3, which are the same.

    I know for a 2nd Order Recurrence Relation with equal roots, the general solution of the relation is C1\lambda^n + C2n\lambda^n, for some constants C1, C2, but what is the general solution for a 3rd Order with equal roots?

    Thankyou.
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  3. #3
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    Hello, jsbach!

    I have a 3rd Order Homogenous Recurrence Relation,
    . . with a characteristic polynomial of: . x^3 - r_1 x^2 - r_2 x - r_3

    This polynomial has three roots: \lambda_1, \lambda_2, \lambda_3, which are equal.

    I know for a 2nd Order Recurrence Relation with equal roots, the general
    solution is: . C_1 \lambda^n + C_2  n \lambda^n, for some constants C_1, C_2.

    But what is the general solution for a 3rd Order with equal roots?

    It is: . C_1 \lambda^n + C_2  n \lambda^n + C_3 n^2 \lambda^n

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