11. Gamma function The gamma function is defined by I (p) = integer. a. Use the reduction formula ["²" to show that I (p+1) = p! (p factorial). x²e-x dx = p f° 00 xP-le-x dx, for p not equal to zero or a negative x XP-lex dx for p = 1, 2, 3, ... G
11. Gamma function The gamma function is defined by I (p) = integer. a. Use the reduction formula ["²" to show that I (p+1) = p! (p factorial). x²e-x dx = p f° 00 xP-le-x dx, for p not equal to zero or a negative x XP-lex dx for p = 1, 2, 3, ... G
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 am confuse how do you solve part a
![111. Gamma function The gamma function is defined by I (p) =
integer.
f(x)=x
a. Use the reduction formula
as48=0
Г(Р) =
to show that I (p+1) = p! (p factorial).
b. Use the substitution x = u² and the fact that
:
Sox
X
00
So xp-¹e* dx → [(p+¹) = P&
-X
↑
u
:
P-1 -X
e
↑
dx
∞
[* pf*:
0
-b
[lim -- XS.
:
£*]
Suv' = uv- Svu
00
P -X
-X
- x-x^ |*" - S^«et pati de
P-1
:
-e
dx
px
M = X
P
_X
= [x²-ë² 10 ] + p Soºč“. ‚x“ d«
Pol
:
dx
·(0)
。)?-.
μ' = px
P
P-1
-X
· [o-o] - Sic². M. de
dx
p
X
Soc. xf² dx
xPex dx = p xP-le-x dx for p = 1, 2, 3, ...
8
foº e
S
∞
v=-èx
': ¿¨*
*x²-¹e-* dx, for p not equal to zero or a negative
√
e-u² du =
to show that I
T ( ²2 ) = √TT.
Suv' = uv-Sve
How to pick .....
IST L
L
од
nverse
A lgebraic (+,-, *, *, `√, x^)
I rig
E xponential](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3073de58-1b40-421a-8538-3fd557e8e327%2F9d96bd61-f9b3-437f-bb1a-1b662c5006d9%2Ffclif5e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:111. Gamma function The gamma function is defined by I (p) =
integer.
f(x)=x
a. Use the reduction formula
as48=0
Г(Р) =
to show that I (p+1) = p! (p factorial).
b. Use the substitution x = u² and the fact that
:
Sox
X
00
So xp-¹e* dx → [(p+¹) = P&
-X
↑
u
:
P-1 -X
e
↑
dx
∞
[* pf*:
0
-b
[lim -- XS.
:
£*]
Suv' = uv- Svu
00
P -X
-X
- x-x^ |*" - S^«et pati de
P-1
:
-e
dx
px
M = X
P
_X
= [x²-ë² 10 ] + p Soºč“. ‚x“ d«
Pol
:
dx
·(0)
。)?-.
μ' = px
P
P-1
-X
· [o-o] - Sic². M. de
dx
p
X
Soc. xf² dx
xPex dx = p xP-le-x dx for p = 1, 2, 3, ...
8
foº e
S
∞
v=-èx
': ¿¨*
*x²-¹e-* dx, for p not equal to zero or a negative
√
e-u² du =
to show that I
T ( ²2 ) = √TT.
Suv' = uv-Sve
How to pick .....
IST L
L
од
nverse
A lgebraic (+,-, *, *, `√, x^)
I rig
E xponential
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