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Tag for the usage of RSolve, RecurrenceTable, DifferenceRoot, and other functions related to difference equations.
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Solving recurrence relations
I have the following recurrence system:
$$\pi_0 =.25\pi_0 + .25q\pi_1+.5q\pi_2 + q\pi_3 $$ $$\pi_1 =.25\pi_0 + .25q\pi_1+.5\pi_2 + p\pi_3 $$ $$\pi_2 =.25\pi_0 + .25p\pi_1+.5p\pi_2
+ 0 $$ $$\pi_3 =. …