In[]:=
Out[]=
0
Coefficient of e:
-
1
5760
2
ϵ
15
4
h
2
ϵ
4
′
z
[α]
+30
4
h
2
ϵ
3
′
z
[α]
(3)
z
[α]+15
2
h
(48+5
2
h
)
2
′′
z
[α]
+
2
h
2
ϵ
4
′′
z
[α]
+
2
h
2
(3)
z
[α]
+4
2
h
′′
z
[α]
(4)
z
[α]+
2
ϵ
3
z[α]
(4(12+
2
h
)
′′
z
[α]+3
2
h
(4)
z
[α])+z[α]4(12+
2
h
)
′′
z
[α]+2
2
h
2
ϵ
3
′′
z
[α]
+3
2
h
(4)
z
[α]+
2
ϵ
2
z[α]
6(8+
2
h
)
2
′′
z
[α]
+
2
h
2
(3)
z
[α]
+4
2
h
′′
z
[α]
(4)
z
[α]+3
2
′
z
[α]
4(-480+20
2
h
+3
4
h
)+
2
ϵ
8(-240+40
2
h
+9
4
h
)
2
z[α]
+10
2
h
z[α](3(16+5
2
h
)
′′
z
[α]+2
2
h
(4)
z
[α])+56
2
h
(8+3
2
h
)
2
′′
z
[α]
+
4
h
2
(3)
z
[α]
+4
4
h
′′
z
[α]
(4)
z
[α]+
2
h
′
z
[α]10(4(-6+
2
h
)+
2
ϵ
((-24+22
2
h
)
2
z[α]
+39
2
h
z[α]
′′
z
[α]+21
2
h
2
′′
z
[α]
))
(3)
z
[α]-3
2
h
(1+
2
ϵ
2
z[α]
)
(5)
z
[α]
Coefficient of e':
0
Coefficient of e'':
0
Coefficient of e''':
0
Coefficient of e'''':
0
Check h^2 z^2 correction to e' coefficient:
0
Check h^2 z^4 correction to e' coefficient:
0
Check h^2 z^2 correction to e'' coefficient:
0
Check h^2 z^4 correction to e'' coefficient:
0
Planar h^4 operator M4[z=0]:
0
Quadratic spherical correction M4[z^2]:
-
ee[α]36
2
′
z
[α]
+154z[α]
′′
z
[α]+5
2
′′
z
[α]
+
2
(3)
z
[α]
+(3z[α]+4
′′
z
[α])
(4)
z
[α]+
′
z
[α](40
(3)
z
[α]-3
(5)
z
[α])
5760
Quartic spherical correction M4[z^4]:
-
1
5760
ee[α]15
3
z[α]
(4
′′
z
[α]+3
(4)
z
[α])+30z[α]
3
′′
z
[α]
+13
′
z
[α]
′′
z
[α]
(3)
z
[α]+
2
′
z
[α]
(15
′′
z
[α]+2
(4)
z
[α])+15
4
′
z
[α]
+
4
′′
z
[α]
+2
3
′
z
[α]
(3)
z
[α]+14
′
z
[α]
2
′′
z
[α]
(3)
z
[α]+
2
′
z
[α]
18
2
′′
z
[α]
+
2
(3)
z
[α]
+4
′′
z
[α]
(4)
z
[α]+
2
z[α]
216
2
′
z
[α]
+156
2
′′
z
[α]
+
2
(3)
z
[α]
+4
′′
z
[α]
(4)
z
[α]+
′
z
[α](220
(3)
z
[α]-3
(5)
z
[α])
Quartic h^4 z^4 coefficient of e:
1
5760
-15
3
z[α]
(4
′′
z
[α]+3
(4)
z
[α])-30z[α]
3
′′
z
[α]
+13
′
z
[α]
′′
z
[α]
(3)
z
[α]+
2
′
z
[α]
(15
′′
z
[α]+2
(4)
z
[α])-15
4
′
z
[α]
+
4
′′
z
[α]
+2
3
′
z
[α]
(3)
z
[α]+14
′
z
[α]
2
′′
z
[α]
(3)
z
[α]+
2
′
z
[α]
18
2
′′
z
[α]
+
2
(3)
z
[α]
+4
′′
z
[α]
(4)
z
[α]-
2
z[α]
216
2
′
z
[α]
+156
2
′′
z
[α]
+
2
(3)
z
[α]
+4
′′
z
[α]
(4)
z
[α]+
′
z
[α](220
(3)
z
[α]-3
(5)
z
[α])
Quartic h^4 z^4 coefficient of e':
0
Quartic h^4 z^4 coefficient of e'':
0
Quartic h^4 z^4 coefficient of e''':
0
Quartic h^4 z^4 coefficient of e'''':
0