Astronomical Applications Department, U.S. Naval Observatory Sensitivity Integral Page 31
doubleprecision t65
t373 = delta**2
t382 = t373**2
t386 = t382**2
t381 = delta*t373
t384 = t381**2
t383 = delta*t382
t374 = nu1**2
t376 = nu1**2*t374**2
t377 = nu1*t376
t378 = nu1*t377
t379 = nu1*t378
t369 = 2.D0*delta
t63 = s**2
t64 = r**2
t65 = g**2
H = (-2520.D0*a4*(330.D0*t384+165.D0*t373+55.D0*t386+330.D0*t381
#+462.D0*t382+11.D0+(462.D0+t383)*t383+(11.D0*t386+55.D0+165.D0*t38
#4)*delta)*nu1*t379-3080.D0*a2*(t373+3.D0*delta+3.D0)*(t384+6.D0*t3
#83+15.D0*t382+21.D0*t381+18.D0*t373+9.D0*delta+3.D0)*t378-3960.D0*
#a0*(t384+7.D0*t383+21.D0*t382+35.D0*t381+35.D0*t373+21.D0*delta+7.
#D0)*t376+(-2772.D0*a3*(t382+3.D0*t381+4.D0*t373+t369+1.D0)*(5.D0+1
#0.D0*delta+10.D0*t373+5.D0*t381+t382)*t379-3465.D0*a1*(t373+t369+2
#.D0)*(t382+4.D0*t381+6.D0*t373+4.D0*delta+2.D0)*t377)*(delta+2.D0)
#)*(t63+t64*(t65+g+1.D0))
return
end
Appendix: Integration Result Expressions
Here is the full expression for the indefinite integration result calculated in
section 2
:
indef
(
)
S , , ,
r s g T
=
+
-
-
-
-
-
-
1
4
a
1
x
1
4
a
0
1
4
a
3
x
3
1
4
a
2
x
2
1
4
a
4
x
4
- -
2 s
r
r g
+
+
3
2
x a
3
3 x
2
a
4
1
2
a
2
(
)
- -
2 s
r
r g
3
6
a
4
(
)
- -
2 s
r
r g
5
(
)
sin (
)
- -
2 s
r
r g x
+
+
+
+
+
+
+
1
4
a
1
x
1
4
a
0
1
4
a
3
x
3
1
4
a
2
x
2
1
4
a
4
x
4
- +
2 s
r
r g
-
-
-
3
2
x a
3
3 x
2
a
4
1
2
a
2
(
)
- +
2 s
r
r g
3
6
a
4
(
)
- +
2 s
r
r g
5
(
)
sin (
)
- +
2 s
r
r g x
+
+
+
+
+
+
+
1
4
a
1
x
1
4
a
0
1
4
a
3
x
3
1
4
a
2
x
2
1
4
a
4
x
4
+ -
2 s
r
r g
-
-
-
3
2
x a
3
3 x
2
a
4
1
2
a
2
(
)
+ -
2 s
r
r g
3
6
a
4
(
)
+ -
2 s
r
r g
5
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