Lecture 18MATH1904

• cours magistral

Lecture 18 MATH1904 Homogeneous Linear Recurrence Relations A k-th order linear recurrence relation for the sequence x0, x1, · · · has the form xn = a1xn−1 + a2xn−2 + · · ·+ akxn−k + fn, for n ≥ k, where a1, a2, . . . , ak are constants and fk, fk+1, fk+2, . . . is some given sequence. We shall restrict our attention to the homogeneous linear recurrence relations: those for which all the fn are 0.

• linear recurrence relations
• function of the sequence
• general solution to the recurrence relation
• homogeneous
• recurrence relation
• partial fraction expansion
• characteristic equation
• initial conditions
• solution