previous case, we can write where Hence, for z # 0, f(z+h)-f(z) -ΣnCnz"-1 =ΣCnbn, h n=0 n=2 If z = 0, bn =h"-1 and the proof follows easily. Otherwise, to obtain a us estimate for bn, we must be a little more careful. Note then that (3) = ¹² „n²|h| |z1² |bn|≤ Σ 2141 bn n(n-1)(n-k+1) k! n n • Σ (²) hk-1₂n-k k=2 k=2 n - < ₁ ² ( x ²² 2₂) n (²2) 14-1²-²212²-(²-2) k-2 for k ≥ 2.
previous case, we can write where Hence, for z # 0, f(z+h)-f(z) -ΣnCnz"-1 =ΣCnbn, h n=0 n=2 If z = 0, bn =h"-1 and the proof follows easily. Otherwise, to obtain a us estimate for bn, we must be a little more careful. Note then that (3) = ¹² „n²|h| |z1² |bn|≤ Σ 2141 bn n(n-1)(n-k+1) k! n n • Σ (²) hk-1₂n-k k=2 k=2 n - < ₁ ² ( x ²² 2₂) n (²2) 14-1²-²212²-(²-2) k-2 for k ≥ 2.
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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