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WZ
Numerade Educator

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Problem 36 Hard Difficulty

The Bessel function of order 1 is defined by
$ J_1 (x) = \sum_{n = 0}^{\infty} \frac {(-1)^n x^{2n + 1}}{n! (n + 1)! 2^{2n + 1}} $
(a) Show that $ J_1 $ satisfies the differential equation
$ x^2 J''_1 (x) + xJ'_1(x) + (x^2 - 1) J_1(x) = 0 $
(b) Show that $ J'_0 (x) = -J_1 (x). $

Answer

a. $0=0$
B. $J_{0}^{\prime}(x)=-J_{1}(x)$

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Video Transcript

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