13. A solution Bessel's equation, x²y" + xy' + (x² – n² )y = 0, , can be found Lna;x)+". One obtains the recurrence relation (n!2")- we get the Bessel function of using the guess y(x) Show that for ao = the first kind of order n from the even valuesj= 2k: -1 7(2n+j) aj aj–2. || (-1)k k!(n + k)! \2 80 X\ n+2k In (x) = E k=0
13. A solution Bessel's equation, x²y" + xy' + (x² – n² )y = 0, , can be found Lna;x)+". One obtains the recurrence relation (n!2")- we get the Bessel function of using the guess y(x) Show that for ao = the first kind of order n from the even valuesj= 2k: -1 7(2n+j) aj aj–2. || (-1)k k!(n + k)! \2 80 X\ n+2k In (x) = E k=0
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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I need help with number 13
Transcribed Image Text:13. A solution Bessel's equation, x²y" + xy' + (x² – n² )y = 0, , can be found
Lna;x)+". One obtains the recurrence relation
(n!2")- we get the Bessel function of
using the guess y(x)
Show that for ao =
the first kind of order n from the even valuesj= 2k:
-1
7(2n+j)
aj
aj–2.
||
(-1)k
k!(n + k)! \2
80
X\ n+2k
In (x) = E
k=0
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