Pi^n/(n!
n
λ
)Sin[Sqrt[λ]r]^(2n)
In[]:=
n
π
-n
λ
2n
Sinr
λ

n!
Out[]=
Series[%,{r,0,4}]
In[]:=
2n
r
λ

n
π
-n
λ
n!
-
(n
n
π
1-n
λ
)
2
r
3n!
+
n(-1+5n)
n
π
2-n
λ
4
r
90n!
+
5
O[r]
Out[]=
Series[Sin[Sqrt[λ]r]^(2n),{r,0,4}]
In[]:=
2n
r
λ

1-
1
3
(nλ)
2
r
+
1
90
(-n
2
λ
+5
2
n
2
λ
)
4
r
+
5
O[r]
Out[]=
Pi^n/(n!
n
λ
)
2n
r
λ

In[]:=
n
π
2n
r
λ

-n
λ
n!
Out[]=
FullSimplify[%,Reals]
In[]:=
n
π
2n
r
λ

-n
λ
n!
Out[]=
FullSimplify[%,{λ>0,r>0}]
In[]:=
n
π
2n
r
n!
Out[]=