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Let f: (0, 00) R be a twice differentiable function satisfying the modified Bessel equation ? f (x) + af' (x) - (2? +1)f(x)
Let f: (0, 00) R be a twice differentiable function satisfying the modified Bessel equation ? f" (x) + af' (x) - (2? +1)f(x) = 0 for all E (0, 00). Prove that if f is not the zero function, then there is at most one point a e (0, 0) with f(a) = 0. Hint: Local extrema.
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An Introduction to Analysis
Authors: William R. Wade
4th edition
132296381, 978-0132296380
