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Starting with the generating function for 1, 2, 3, 4, ..., find a generating function for each of the following sequences. а. 1,0, 2, 0, 3, 0, 4,.... b. 1, -2,3, –4, 5, –6, .... с. 0,3, 6, 9, 12, 15, 18, ....

Starting with the generating function for 1, 2, 3, 4, ..., find a generating function for each of the following sequences. а. 1,0, 2, 0, 3, 0, 4,.... b. 1, -2,3, –4, 5, –6, .... с. 0,3, 6, 9, 12, 15, 18, ....

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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· Starting with the generating function for 1,2, 3, 4, ..., find a generating function for each of the following sequences. а. 1,0, 2,0, 3, 0, 4,.... b. 1,–2,3, –4, 5, –6, .... с. 0,3, 6, 9, 12, 15, 18, .... d. 0,3,9, 18, 30, 45, 63, .... (Hint: relate this sequence to the previous one.) v Solution *** . а. (1-z*)2 1 b. (1+1) * C. (1-z)2 d. (1-z)* (partial sums).
Transcribed Image Text:· Starting with the generating function for 1,2, 3, 4, ..., find a generating function for each of the following sequences. а. 1,0, 2,0, 3, 0, 4,.... b. 1,–2,3, –4, 5, –6, .... с. 0,3, 6, 9, 12, 15, 18, .... d. 0,3,9, 18, 30, 45, 63, .... (Hint: relate this sequence to the previous one.) v Solution *** . а. (1-z*)2 1 b. (1+1) * C. (1-z)2 d. (1-z)* (partial sums).
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