2. The Bessel function of order 1 is (-1)*22k 22k+1 k!(k+1)! J1 (x) = x Lk=0 (a) Show that the series converges for all x. (b) Show that the series is a solution of the differential equation x² J" + xJ{ + (x² – 1) J1 = 0. (c) The - Bessel function of order 0 is (-1)*22k Jo (x) = Ek=0 2k (k!)² Show that Jó (x) = –J1 (x).
2. The Bessel function of order 1 is (-1)*22k 22k+1 k!(k+1)! J1 (x) = x Lk=0 (a) Show that the series converges for all x. (b) Show that the series is a solution of the differential equation x² J" + xJ{ + (x² – 1) J1 = 0. (c) The - Bessel function of order 0 is (-1)*22k Jo (x) = Ek=0 2k (k!)² Show that Jó (x) = –J1 (x).
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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