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Find a power series representation (at base point O) for the function f(x) = x³ In(1-x²) 4 You do not need to find the interval of convergence. Hint: Use common Taylor series. It will not be productive to take derivatives! O ∞ f(x) = (-1)+1. n=1 f(x) = - Σ n=1 ° ∞ x²n+3 n=1 n x²n f(x) = (-1)". 3n x²n+3 ∞ f(x) = Σ(1)" . n=1 xn 6n n

Find a power series representation (at base point O) for the function f(x) = x³ In(1-x²) 4 You do not need to find the interval of convergence. Hint: Use common Taylor series. It will not be productive to take derivatives! O ∞ f(x) = (-1)+1. n=1 f(x) = - Σ n=1 ° ∞ x²n+3 n=1 n x²n f(x) = (-1)". 3n x²n+3 ∞ f(x) = Σ(1)" . n=1 xn 6n n

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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Find a power series representation (at base point O) for the function ƒ(x) = x³ ln(1 – x²) 4 You do not need to find the interval of convergence. Hint: Use common Taylor series. It will not be productive to take derivatives! O O f(x) = Σ(−1)n+1 f(x) n=1 0 f(x) = Σ(1)" n=1 x2n+3 Στη n n=1 x²n+3 n=1 x²n 3n f(x) = (-1)n an 6n
Transcribed Image Text:Find a power series representation (at base point O) for the function ƒ(x) = x³ ln(1 – x²) 4 You do not need to find the interval of convergence. Hint: Use common Taylor series. It will not be productive to take derivatives! O O f(x) = Σ(−1)n+1 f(x) n=1 0 f(x) = Σ(1)" n=1 x2n+3 Στη n n=1 x²n+3 n=1 x²n 3n f(x) = (-1)n an 6n
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