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the Maclaurin series for the function in another way: Assume that f(x):= X 1-x-x² = Scan. n=0 ply both sides of the equation above by 1 − x − x². Show that the coefficients cn must satisfy elationship: Cn+1 = Cn + Cn-1.

the Maclaurin series for the function in another way: Assume that f(x):= X 1-x-x² = Scan. n=0 ply both sides of the equation above by 1 − x − x². Show that the coefficients cn must satisfy elationship: Cn+1 = Cn + Cn-1.

Advanced Engineering Mathematics
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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Solve the part b

A generating function for a sequence (cn) is a function f(x) with a power series representation: f(x) = Σ cnan n=0
Transcribed Image Text:A generating function for a sequence (cn) is a function f(x) with a power series representation: f(x) = Σ cnan n=0
b. Find the Maclaurin series for the function in another way: Assume that Σ n=0 f(x) = = Xx 1- x x² = n Multiply both sides of the equation above by 1 - x - x². Show that the coefficients cn must satisfy the relationship: Cn+1 = Cn + Cn-1.
Transcribed Image Text:b. Find the Maclaurin series for the function in another way: Assume that Σ n=0 f(x) = = Xx 1- x x² = n Multiply both sides of the equation above by 1 - x - x². Show that the coefficients cn must satisfy the relationship: Cn+1 = Cn + Cn-1.
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