A linear homogeneous recurrence relation with constant coefficients of degree 9 has the general solution Indicate the multiplicity of the root 9.
A linear homogeneous recurrence relation with constant coefficients of degree 9 has the general solution Indicate the multiplicity of the root 9.
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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A linear homogeneous recurrence relation with constant coefficients of degree 9 has the general solution
Indicate the multiplicity of the root 9.
![The image contains the following mathematical expression:
\[
(\alpha_{10} + \alpha_{11} n)(-2)^n + (\alpha_{20} + \alpha_{21} n + \alpha_{22} n^2)(7)^n + (\alpha_{30} + \alpha_{31} n + \alpha_{32} n^2 + \alpha_{33} n^3)(9)^n
\]
This expression seems to be a polynomial function where different terms are multiplied by powers of different constants (-2, 7, and 9). Each term is multiplied by a polynomial in \(n\), indicated by the coefficients \(\alpha_{ij}\), where \(i\) denotes the term number and \(j\) the degree of \(n\) in that term. The expression is useful for understanding how polynomial functions can be constructed with different bases raised to the power of \(n\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3632b9ca-0e22-48c8-943d-c9e08fc0f04c%2F7b5b38d9-7e19-4d9c-ba47-138b1c0064e2%2Fsvmj6rw_processed.png&w=3840&q=75)
Transcribed Image Text:The image contains the following mathematical expression:
\[
(\alpha_{10} + \alpha_{11} n)(-2)^n + (\alpha_{20} + \alpha_{21} n + \alpha_{22} n^2)(7)^n + (\alpha_{30} + \alpha_{31} n + \alpha_{32} n^2 + \alpha_{33} n^3)(9)^n
\]
This expression seems to be a polynomial function where different terms are multiplied by powers of different constants (-2, 7, and 9). Each term is multiplied by a polynomial in \(n\), indicated by the coefficients \(\alpha_{ij}\), where \(i\) denotes the term number and \(j\) the degree of \(n\) in that term. The expression is useful for understanding how polynomial functions can be constructed with different bases raised to the power of \(n\).
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