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Prove that the function 1 f: (1, co) → R, x + n=1 is infinitely differentiable. (Do this by showing that the series, and all its derivatives, are uniformly convergent on (a, ∞) for any fixed a > 1, and appeal to the relevant theorems. ) -

Prove that the function 1 f: (1, co) → R, x + n=1 is infinitely differentiable. (Do this by showing that the series, and all its derivatives, are uniformly convergent on (a, ∞) for any fixed a > 1, and appeal to the relevant theorems. ) -

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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Prove that the function 00 f: (1, co) → R, x > Σ n=1 is infinitely differentiable. (Do this by showing that the series, and all its derivatives, are uniformly convergent on (a, 0) for any fixed a > 1, and appeal to the relevant theorems. )
Transcribed Image Text:Prove that the function 00 f: (1, co) → R, x > Σ n=1 is infinitely differentiable. (Do this by showing that the series, and all its derivatives, are uniformly convergent on (a, 0) for any fixed a > 1, and appeal to the relevant theorems. )
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