Answered: Show that if a+ bª and n is a power of…

Show that if a+ bª and n is a power of b, then f(n) = C,nd +C,n®$» «, wherp C = b*c/(bt – a) and C, = F(1) + b'c/(a – b).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Assume that f is an increasing function satisfying the recurrence relation f (n) = af (n∕b) + cn^d, where a ≥ 1, b is an integer greater than 1, and c and d are positive real numbers

Show that if a+ bª and n is a power of b, then f(n) =
C,nd +C,n®$» «, wherp C = b*c/(bt – a) and C, =
F(1) + b'c/(a – b).

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