In[]:=
ANS1=FullSimplifyAssuming(0<θ<π)&&(l∈PositiveIntegers)&&(l≥0)&&(
r
0
∈PositiveReals)&&(r∈PositiveReals),Limit
LegendreP[1+2l,1,Cos[θ]]
-1-2l
(γ
r
0
)
-
l
(-1)
-
5
2
-l
2
π
BesselJ
3
2
+2l,rγ(-1+2l)!!(3+4l)!!
(1+l)!
rγ
,γ0
Out[]=
-
l
(-1)
-4-3l
2
π
(-1+2l)!!(3+4l)!!LegendreP[1+2l,1,Cos[θ]]
1+2l
r
r
0
Gamma[2+l]Gamma
5
2
+2l