Why use the hypothesis of n=m-1 with a step-by-step explanation of the solution and a clear line, please Since (m-1)! = * Ohen m=0 A50, the tem yresponding to m=o vanisnes Therepre Changing tue variable of Summation to n=m -1 (リn+」 Σ m!r(n+v+2) an+V+1 2n+1 0ニ4 2n+ V+1 - V (-1)" x n=o n! rn+l +v+1) 2 2n+V+1 - リnx2h+V+1 iu 3 2n+V+1 r (n+l+v+1) ーズV レ+」(x) ッ+ Hence a [zVI, x)] =-xJvi (x) Hence [zJ, (x)] = -* ニーメJvti x) (Proved) %3D

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Why use the hypothesis of n=m-1
with a step-by-step explanation of
the solution and a clear line, please
= 0 Ohen m = 0 ASo, the term yresponding
Since (m-1)!
to m=o vanisnes
Therepre Changimg tue variable of Summation to n=m -1
2n+1
Σ
n=0 n!r(n+v+2) 2an+V+1
2n+ V+1
8.
- V
(-1)" x
Σ
n=a n! P(n+l +v+1) 22n+v+1
* (-n x2h+V+1
2n+V+)
r (nti+v+1)
n=0
3
ーズ
レ+」(x)
Jutl
-V
Hence a [zVJ, (x)] = -x JvH (x)
(Proved)
%3D
Transcribed Image Text:Why use the hypothesis of n=m-1 with a step-by-step explanation of the solution and a clear line, please = 0 Ohen m = 0 ASo, the term yresponding Since (m-1)! to m=o vanisnes Therepre Changimg tue variable of Summation to n=m -1 2n+1 Σ n=0 n!r(n+v+2) 2an+V+1 2n+ V+1 8. - V (-1)" x Σ n=a n! P(n+l +v+1) 22n+v+1 * (-n x2h+V+1 2n+V+) r (nti+v+1) n=0 3 ーズ レ+」(x) Jutl -V Hence a [zVJ, (x)] = -x JvH (x) (Proved) %3D
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