... 1 Suppose that for i = 1,2, m the function fi is real valued on the interval [a, b] of the form that, for every i, there exists a sequence of polynomials that uniformly converges to fi in [a, b]. Prove that there also exists a sequence of polynomials that converges uniformly to the product function f₁f2 fm on [a, b].

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Suppose that for i = 1,2, ..., m the function fi is real valued on the interval [a, b] of the
form that, for every i, there exists a sequence of polynomials that uniformly converges to fi
in [a, b]. Prove that there also exists a sequence of polynomials that converges uniformly to
the product function f₁f₂ fm on [a, b].
Transcribed Image Text:Suppose that for i = 1,2, ..., m the function fi is real valued on the interval [a, b] of the form that, for every i, there exists a sequence of polynomials that uniformly converges to fi in [a, b]. Prove that there also exists a sequence of polynomials that converges uniformly to the product function f₁f₂ fm on [a, b].
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