MATHS I -
Special functions
Kamma ]
beta, Jacobian ,
,
generating function
Shreya Prasad
,Gamma function :
rcn )=fé% an-1dm
Alternate fame :
og(
"'
i. rent -
-
du
Ñn2n -1dm
•
2£
2. rln ) =
e-
Beta function :
1
f. am
-
' ^^
Blm ,n)= d- a) du
Alternate forms :
,n)=§°ym
•
l
/yn.io#mtndY
-
1.
Blm Mindy or
☒
1172
7-pCn.m
2. Blm ,ñ=
)
Relationships between Beta and Gamma functions :
I. BIM .nl =
rcm ) rln) .
4m¥
rln) ra n )
¥mn#
2. - - =
o.ir#-.rt
, Bessel function :
Jnu )=F C- Dr
2mn
[ Hrcn+ (f)
F- 0
ttdethaleforms :
1 .
Ink )= C- In Jnln )
formulas :
Jn 11N ))
1. nJnCN= GIN -111Mt -
2. Jica )= § (Jn ith) Jatin ))
-
-
Jna , (a)
'
N Jn th ) NJ , Ia ) n
-
=
3.
4. Mtn 'M ) =
NJn.fm nJnCn)
-
Jntk ) ) k^Jn -11N
got
5. =
ÑnJn-111k )
6.
ddncñ"JnCnD
= -
NOTE :
JOIN = 1-
(E)
2 -1
(E)
4
-
gf, (f) ,
'
+ . - -
sfimilasitieswithcossif
JIM =
I
-
off +2,7¥
-
- -
-
[similarities with sima]
Special functions
Kamma ]
beta, Jacobian ,
,
generating function
Shreya Prasad
,Gamma function :
rcn )=fé% an-1dm
Alternate fame :
og(
"'
i. rent -
-
du
Ñn2n -1dm
•
2£
2. rln ) =
e-
Beta function :
1
f. am
-
' ^^
Blm ,n)= d- a) du
Alternate forms :
,n)=§°ym
•
l
/yn.io#mtndY
-
1.
Blm Mindy or
☒
1172
7-pCn.m
2. Blm ,ñ=
)
Relationships between Beta and Gamma functions :
I. BIM .nl =
rcm ) rln) .
4m¥
rln) ra n )
¥mn#
2. - - =
o.ir#-.rt
, Bessel function :
Jnu )=F C- Dr
2mn
[ Hrcn+ (f)
F- 0
ttdethaleforms :
1 .
Ink )= C- In Jnln )
formulas :
Jn 11N ))
1. nJnCN= GIN -111Mt -
2. Jica )= § (Jn ith) Jatin ))
-
-
Jna , (a)
'
N Jn th ) NJ , Ia ) n
-
=
3.
4. Mtn 'M ) =
NJn.fm nJnCn)
-
Jntk ) ) k^Jn -11N
got
5. =
ÑnJn-111k )
6.
ddncñ"JnCnD
= -
NOTE :
JOIN = 1-
(E)
2 -1
(E)
4
-
gf, (f) ,
'
+ . - -
sfimilasitieswithcossif
JIM =
I
-
off +2,7¥
-
- -
-
[similarities with sima]
