Java Printing

z s C1 , s=0 s g 1 1 1 1 K2 2 3 4 5 s C Kg 1 C g 2 sK g 3 s C g 4 s K g 5 s CO s s 2 6 24 120

> series

(1)

s

x z s C2 $ Q > D1I1 d diff ,s : z s C3 $ s C1 $ s C2 s x z s C2 $ Q g1I1 d : z s C3 $ s C1 $ s C2 Res1I1 d subs s = 0, D1I1$1 Cg1I1$g 1 z 2 g 1 z 1, 2 Res1I1 := C 2 z 3 2 z 3

1 C 2

z 2 ln

x Q

K

z 3

z s C2 , s =K1 s C1 g 1 1 K2 s C1 C Kg 1 C g 2 s C1 K g 3 s C1 2 6 1 4 5 K g 5 s C1 CO s C1 120

1 z 2 z 1, 3 2 2 z 3

K

3 z 2 4 z 3

(2)

> series

s C1

2

C

1 g 4 24

s C1

3

(3)

s

x Q > D2I1 d diff ,s : z s C3 $s$ s C2 s x z s C1 $ Q g2I1 d : z s C3 $s$ s C2 Res2I1 d subs s =K1, D2I1$1 Cg2I1$g z s C1 $

Res2I1 := K

z 0 Qg xz 2

K

z 1, 0 Q xz 2

z 0 Q ln K

x Q

C

xz 2

z 0 Q z 1, 2 xz 2

2

(4)

s

x Q > D1I2 d diff ,s : z s C3 $ s C1 $ s C2 s x z 1, s C2 $ Q g1I2 d : z s C3 $ s C1 $ s C2 Res1I2 d subs s = 0, D1I2$1 Cg1I2$g z 1, s C2 $

Res1I2 :=

1 z 1, 2 g 1 z 2, 2 C 2 2 z 3 z 3

C

1 2

z 1, 2 ln z 3

x Q

K

1 z 1, 2 z 1, 3 2 2 z 3

(5)

K

3 z 1, 2 4 z 3

z 1, s C2 , s =K1 s C1 g 1 1 K3 K s C1 K Cg 2 K g 3 s C1 2 1 4 C g 6 s C1 CO s C1 120 > series

s C1 C

1 g 4 6

2

s C1

K

1 g 5 24

s C1

3

(6)

5 s

x z s C1 $ Q > D2I2 d diff diff ,s ,s : z s C3 $s$ s C2 s x z s C1 $ Q g2I2 d : z s C3 $s$ s C2 D2I2 Res2I2 d subs s =K1, $ K1 Cg2I2$ Kg 1 2 x x z 0 Q ln z 1, 2 z 0 Q ln Q 1 Q Res2I2 := K C 2 2 xz 2 xz 2 K C

z 1, 0 Q z 1, 2 2

xz 2

z 1, 0 Q ln C

x Q

K

xz 2

C

z 0 Q z 1, 2 xz 2

1 z 0 Q z 2, 2 2 2 xz 2

C

2

3

(7)

z 0 Q xz 2

z 0 Qg 1 1 z 2, 0 Q C 2 xz 2 xz 2 z s C2 $ z 1, s C3 $

> D1I3 d diff

z s C3

x Q

s

,s :

2

$ s C1 $ s C2 s x z s C2 $ z 1, s C3 $ Q g1I3 d : 2 z s C3 $ s C1 $ s C2 Res1I3 d subs s = 0, D1I3$1 Cg1I3$g

Res1I3 :=

K

2

1 z 2 z 1, 3 g 1 z 1, 2 z 1, 3 C 2 2 2 2 z 3 z 3

z 2 z 1, 3 z 3

> D2I3 d diff

3

2

K

3 z 2 z 1, 3 2 4 z 3

C

x z s C1 $ z 1, s C3 $ Q z s C3

2

$s$ s C2

C

1 2

z 2 ln

1 z 2 z 2, 3 2 2 z 3 s

,s :

x Q z 3

z 1, 3 2

(8)

g2I3 d

s

x Q

z s C1 $ z 1, s C3 $ 2

z s C3 $s$ s C2 Res2I3 d subs s =K1, D2I3$1 Cg2I3$g Res2I3 := K

C

z 0 Q z 1, 2 g 2

xz 2

2 z 0 Q z 1, 2 xz 2

2

3

K

K

xz 2

> D2I4 d diff

x Q

xz 2

z 1, 2 (9)

2

z 0 Q z 2, 2 2

xz 2

1 z 2 g 1 z 1, 2 C 4 z 3 4 z 3 z s C1 $

K

2

s

2

z s C3 $ s C1 $ s C2 s x z s C2 $ Q g1I4 d : 2 z s C3 $ s C1 $ s C2 Res1I4 d subs s = 0, D1I4$1 Cg1I4$g

Res1I4 :=

z 0 Q ln

z 1, 0 Q z 1, 2

x z s C2 $ Q

> D1I4 d diff

:

x Q

C

,s :

z 2 ln

1 4

x Q

K

z 3

1 z 2 z 1, 3 2 4 z 3

1 z 2 2 z 3

K

(10)

s

,s : 2 z s C3 $s$ s C2 s x z s C1 $ Q g2I4 d : 2 z s C3 $s$ s C2 Res2I4 d subs s =K1, D2I4$1 Cg2I4$g Res2I4 := K

z 0 Qg xz 2

K

z 1, 0 Q xz 2

z 0 Q ln K

x Q

C

xz 2

z 0 Q z 1, 2 xz 2

2

C

z 0 Q xz 2

(11)

s

x Q > D1I5 d diff ,s : z s C3 $ s C1 $ s C2 s x z 2, s C2 $ Q g1I5 d : z s C3 $ s C1 $ s C2 Res1I5 d subs s = 0, D1I5$1 Cg1I5$g z 2, s C2 $

1 z 2, 2 g 1 z 3, 2 Res1I5 := C 2 2 z 3 z 3

1 C 2

z 2, 2 ln z 3

x Q

K

1 z 2, 2 z 1, 3 2 2 z 3

(12)

K

3 z 2, 2 4 z 3

z 2, s C2 , s =K1 s C1 g 2 1 K4 2 s C1 C Kg 3 C g 4 s C1 2 1 4 K g 7 s C1 CO s C1 120 > series

s C1 K

1 g 5 6

2

s C1

1 g 6 24

C

s C1

3

(13)

5 s

x z s C1 $ Q ,s ,s ,s : z s C3 $s$ s C2

> D2I5 d diff diff diff

s

x Q g2I5 d : z s C3 $s$ s C2 D2I5 Res2I5 d subs s =K1, $ 2 Cg2I5$g 2 6 z s C1 $

Res2I5 := K

2 z 1, 0 Q 1 z 3, 0 Q K K 3 xz 2 xz 2

C

K

C

C

xz 2

z 1, 2

xz 2

2 z 0 Q z 1, 2 4

xz 2

z 2, 0 Q z 1, 2 2

xz 2

xz 2

K

3

x Q

3

C

C

z 0 Qg 2

z s C3

K

xz 2

z 1, 0 Q z 2, 2 xz 2

2

xz 2

1 3

2

$ s C1 $ s C2

2

(14)

3

z 1, 2

z 0 Q ln C

z 0 Q ln

x Q

xz 2

z 2, 2 2

3

x Q

xz 2

2

K

2 z 1, 0 Q z 1, 2 xz 2

z 2, 0 Q ln K

2

x Q

z 1, 2

2

2 z 0 Q z 1, 2

z 1, s C2 $z 1, s C3 $ > D1I6 d diff

x Q

xz 2

x z 1, 0 Q ln Q K xz 2

x Q

xz 2

2 z 1, 0 Q ln C

2

2 z 0 Q z 1, 2 z 2, 2

2 z 0 Q ln K

2

x Q

z 0 Q ln

2 z 0 Q ln

s

,s :

xz 2

2

3

x Q

C

1 z 0 Q z 3, 2 2 3 xz 2

x Q

z 1, s C2 $z 1, s C3 $ g1I6 d

s

:

2

z s C3 $ s C1 $ s C2 Res1I6 d subs s = 0, D1I6$1 Cg1I6$g

1 z 1, 2 z 1, 3 g 1 z 2, 2 z 1, 3 Res1I6 := C 2 2 2 2 z 3 z 3 K

z 1, 2 z 1, 3 z 3

2

3 z 1, 2 z 1, 3 2 4 z 3

K

3

z s C3

z s C1 $z 1, s C3 $ z s C3

s

:

2

K

xz 2

3

2

C

1 z 2, 0 Q z 1, 2 2 2 xz 2

C

2

z 1, 2 (16)

2

z 1, 0 Q z 2, 2 2

xz 2 x z 1, 0 Q ln z 1, 2 Q

z 0 Q z 1, 2 1 z 0 Q z 3, 2 C C 2 2 2 xz 2 xz 2 x z 0 Q ln z 2, 2 3 z 0 Q z 1, 2 Q C C 2 4 xz 2 xz 2 C

C

(15)

,s ,s :

$s$ s C2

$s$ s C2 D2I6 Res2I6 d subs s =K1, $ K1 Cg2I6$ Kg 1 2 2 x x 2 z 0 Q ln z 1, 2 z 0 Q ln Q 1 Q Res2I6 := K C 3 2 xz 2 xz 2 2 z 1, 0 Q z 1, 2

2

1 z 1, 2 z 2, 3 2 2 z 3

2

x Q

z 3

z 1, 3

s

x z s C1 $z 1, s C3 $ Q

> D2I6 d diff diff

g2I6 d

C

x Q

z 1, 2 ln

1 C 2

xz 2 3

K

2

3 z 0 Q z 1, 2 z 2, 2 xz 2

3

z 0 Q z 1, 2 g 1 xz 2

2

z 1, s C2 $ > D1I7 d diff

x Q

s

z s C3 $ s C1 $ s C2 s x z 1, s C2 $ Q g1I7 d : 2 z s C3 $ s C1 $ s C2 Res1I7 d subs s = 0, D1I7$1 Cg1I7$g

2

,s :

(17)

1 z 1, 2 g 1 z 2, 2 Res1I7 := C 4 4 z 3 z 3 K

C

z 1, 2 ln

1 4

> D2I7 d diff diff

z 3

x Q

1 z 0 Q z 2, 2 2 2 xz 2 x Q

z 0 Q ln xz 2

K

z 1, 0 Q

1 C 2

xz 2

> D1I8 d diff

z s C3

2z 0 Q

C

z 0 Q ln

xz 2

(17)

x Q

3

3 z 2 z 2, 3 2 4 z 3

z s C1 $z 2, s C3 $ > D2I8 d diff

z s C3

2

$s$ s C2

x Q

2

(18)

z 0 Q z 1, 2 1 z 2, 0 Q C 2 2 xz 2 xz 2 2

xz 2

C

3

z 0 Qg 1 xz 2

,s :

1 z 2 z 2, 3 g 1 z 1, 2 z 2, 3 Res1I8 := C 2 2 2 2 z 3 z 3 z 3

xz 2

s

2

K

z 1, 0 Q z 1, 2

z 0 Q z 1, 2

C

$ s C1 $ s C2 s x z s C2 $z 2, s C3 $ Q g1I8 d : 2 z s C3 $ s C1 $ s C2 Res1I8 d subs s = 0, D1I8$1 Cg1I8$g

z 2 z 2, 3 z 1, 3

C

K

2

x Q

xz 2

z s C2 $z 2, s C3 $

K

1 z 1, 2 z 1, 3 2 4 z 3

s

,s ,s : 2 z s C3 $s$ s C2 s x z s C1 $ Q g2I7 d : 2 z s C3 $s$ s C2 D2I7 Res2I7 d subs s =K1, $ K1 Cg2I7$ Kg 1 2 x x z 0 Q ln z 1, 2 z 1, 0 Q ln Q Q Res2I7 := K C 2 xz 2 xz 2

K

K

1 z 1, 2 2 z 3 z s C1 $

K

x Q

1 C 2 C

s

,s :

x Q

z 2 ln

z 3

1 z 2 z 3, 3 2 2 z 3

z 2, 3 2

(19)

z s C1 $z 2, s C3 $ g2I8 d

x Q

s

:

2

z s C3 $s$ s C2 Res2I8 d subs s =K1, D2I8$1 Cg2I8$g Res2I8 := K C

z 0 Q z 2, 2 g

K

2

xz 2

2 z 0 Q z 1, 2 z 2, 2 xz 2

K

3

s

x Q

2

$

,s :

$ s C1 $ s C2 s 2 x z s C2 $ z 1, s C3 $ Q g1I9 d : 3 z s C3 $ s C1 $ s C2 Res1I9 d subs s = 0, D1I9$1 Cg1I9$g

Res1I9 :=

K

1 z 2 z 1, 3 3 2 z 3

3 z 2 z 1, 3 4 2 z 3

2

g

3

C

g2I9 d

2

z s C3

C

$

3

z s C3 $s$ s C2 Res2I9 d subs s =K1, D2I9$1 Cg2I9$g Res2I9 := K

C

z 0 Q z 1, 2 xz 2

3 z 0 Q z 1, 2 xz 2

4

2

g

3 3

K

K

z s C2 $z 1, s C3 $ > D1I10 d diff

z s C3

2

(21)

3

z 2 z 2, 3 z 1, 3 z 3

3

z 0 Q ln

2

K

3

2 z 0 Q z 1, 2 z 2, 2 xz 2

2

:

z 1, 0 Q z 1, 2 xz 2

z 3

z 1, 3

,s :

3

$s$ s C2 s 2 x z s C1 $ z 1, s C3 $ Q

1 2

C

x Q

z 2 ln

s

x Q

2

z s C1 $ z 1, s C3 > D2I9 d diff

2

1 z 1, 2 z 1, 3 3 2 z 3

3 z 2 z 1, 3 3 4 z 3

K

(20)

2

2

xz 2

3

z s C3

xz 2

z 2, 2

z 0 Q z 3, 2

z s C2 $ z 1, s C3 > D1I9 d diff

K

2

xz 2

x Q

z 0 Q ln

z 1, 0 Q z 2, 2

3

x Q

$ s C1 $ s C2

s

2

,s :

x Q

xz 2

z 1, 2 3

2

(22)

x Q

z s C2 $z 1, s C3 $ g1I10 d

s

2

2

z s C3 $ s C1 $ s C2 Res1I10 d subs s = 0, D1I10$1 Cg1I10$g

:

1 z 2 z 1, 3 g 1 z 1, 2 z 1, 3 Res1I10 := C 2 2 4 4 z 3 z 3 K

1 z 2 z 1, 3 3 2 z 3

> D2I10 d diff

2

K

1 z 2 z 1, 3 2 2 z 3

2

z s C3

2

2

z 3

z 1, 3 (23)

2

1 z 2 z 2, 3 2 4 z 3

s

x z s C1 $z 1, s C3 $ Q

$s$ s C2 s x z s C1 $z 1, s C3 $ Q

g2I10 d

C

x Q

z 2 ln

1 C 4

,s :

2

:

z s C3 $s$ s C2 Res2I10 d subs s =K1, D2I10$1 Cg2I10$g Res2I10 := K

C

z 0 Q z 1, 2 g xz 2

2

2 z 0 Q z 1, 2

2

xz 2

3

C

z 1, 0 Q z 1, 2

K

2

xz 2

z 0 Q z 1, 2 xz 2

z s C2 $ > D1I11 d diff

x Q

K

2

3

1 z 2 g 1 z 1, 2 C 8 z 3 8 z 3 z s C1 $

> D2I11 d diff

x Q

K

x Q

xz 2

z 1, 2 (24)

2

z 0 Q z 2, 2 xz 2

2

s

z s C3 $ s C1 $ s C2 s x z s C2 $ Q g1I11 d : 3 z s C3 $ s C1 $ s C2 Res1I11 d subs s = 0, D1I11$1 Cg1I11$g

Res1I11 :=

z 0 Q ln

C

1 8

,s :

z 2 ln

s

,s : 3 z s C3 $s$ s C2 s x z s C1 $ Q g2I11 d : 3 z s C3 $s$ s C2 Res2I11 d subs s =K1, D2I11$1 Cg2I11$g

z 3

x Q

K

1 z 2 z 1, 3 2 8 z 3

K

5 z 2 16 z 3

(25)

Res2I11 := K

z 0 Qg xz 2

z 1, 0 Q

K

xz 2

x Q

z 0 Q ln K

C

xz 2

z 0 Q z 1, 2 xz 2

2

C

2z 0 Q xz 2

(26)

s

x $diff G s C2 , s Q > D1I12 d diff ,s : z s C3 $ s C1 $ s C2 $G s C2 s x z s C2 $ $diff G s C2 , s Q g1I12 d : z s C3 $ s C1 $ s C2 $G s C2 Res1I12 d subs s = 0, D1I12$1 Cg1I12$g z s C2 $

1 z 2 Y 2 g 1 z 1, 2 Y 2 Res1I12 := C 2 2 z 3 z 3 C

1 z 2 Y 1, 2 2 z 3

K

C

1 z 2 Y 2 z 1, 3 2 2 z 3

1 2

K

z 2 ln

x Q z 3

Y 2 (27)

3 z 2 Y 2 4 z 3

s

x $diff G s C2 , s Q > D2I12 d diff ,s : z s C3 $s$ s C2 $G s C2 s x z s C1 $ $diff G s C2 , s Q g2I12 d : z s C3 $s$ s C2 $G s C2 Res2I12 d subs s =K1, D2I12$1 Cg2I12$g z s C1 $

Res2I12 := K K

z 0 QY 1 g xz 2

z 0 Q Y 1, 1 xz 2

C

K

z 1, 0 Q Y 1 xz 2

x Q xz 2

z 0 Q ln K

Y 1 (28)

z 0 Q Y 1 z 1, 2 xz 2

2

s

x $diff G s C2 , s Q > D1I13 d diff ,s : z s C3 $ s C1 $ s C2 $G s C2 s x z 1, s C2 $ $diff G s C2 , s Q g1I13 d : z s C3 $ s C1 $ s C2 $G s C2 Res1I13 d subs s = 0, D1I13$1 Cg1I13$g z 1, s C2 $

1 z 1, 2 Y 2 g 1 z 2, 2 Y 2 Res1I13 := C 2 2 z 3 z 3 C

1 z 1, 2 Y 1, 2 2 z 3

K

1 C 2

1 z 1, 2 Y 2 z 1, 3 2 2 z 3

x Q z 3

z 1, 2 ln

K

3 z 1, 2 Y 2 4 z 3

Y 2 (29)

s

x $diff G s C2 , s Q ,s ,s : z s C3 $s$ s C2 $G s C2

z s C1 $ > D2I13 d diff diff

s

x $diff G s C2 , s Q g2I13 d : z s C3 $s$ s C2 $G s C2 D2I13 Res2I13 d subs s =K1, $ K1 Cg2I13$ Kg 1 2 x z 0 Q ln Y 1 z 1, 2 z 0 Q Y 1 z 1, 2 Q Res2I13 := K C 2 3 xz 2 xz 2 z s C1 $

C K

z 1, 0 Q Y 1, 1 xz 2

1 z 0 Q Y 2, 1 2 xz 2

z 1, 0 Q Y 1 z 1, 2 xz 2 z 1, 0 Q ln

C C

C

x Q

xz 2

Y 1 C

xz 2

(30)

K

Y 1, 1

1 z 0 Q Y 1 z 2, 2 2 2 xz 2 1 C 2

2

x Q xz 2

z 0 Q ln

Y 1

z 0 QY 1 g 1 xz 2 z s C2 $z 1, s C3 $

> D1I14 d diff

g1I14 d

z s C3

x Q

s

$diff G s C2 , s

2

$ s C1 $ s C2 $G s C2 s x z s C2 $z 1, s C3 $ $diff G s C2 , s Q

: 2 z s C3 $ s C1 $ s C2 $G s C2 Res1I14 d subs s = 0, D1I14$1 Cg1I14$g 1 z 2 Y 2 z 1, 3 g 1 z 1, 2 Y 2 z 1, 3 Res1I14 := C 2 2 2 2 z 3 z 3 x z 2 ln Y 2 z 1, 3 1 Q 1 z 2 Y 1, 2 z 1, 3 C C 2 2 2 2 z 3 z 3 K

1 z 2, 0 Q Y 1 2 xz 2

xz 2

2

x Q xz 2

z 0 Q ln

C

z 0 QY 1

z 0 Q Y 1, 1 z 1, 2

K

2

C

2

3 z 2 Y 2 z 1, 3 2 4 z 3

C

(31)

K

z 2 Y 2 z 1, 3

1 z 2 Y 2 z 2, 3 2 2 z 3

z s C1 $z 1, s C3 $ > D2I14 d diff

,s :

z s C3

2

x Q

s

$diff G s C2 , s

$s$ s C2 $G s C2

,s :

z 3

3

2

g2I14 d

s

x Q

z s C1 $z 1, s C3 $

$diff G s C2 , s

2

z s C3 $s$ s C2 $G Res2I14 d subs s =K1, D2I14$1 Cg2I14$g z 0 Q Y 1 z 1, 2 g z 1, 0 Res2I14 := K K 2 xz 2 x z 0 Q ln Y 1 z 1, 2 z 0 Q K K 2 xz 2 K

:

s C2 Q Y 1 z 1, 2 xz 2

Q Y 1, 1 z 1, 2 xz 2

xz 2

xz 2

2

3

2

> D1I15 d diff

x Q

s

$diff G s C2 , s 2

z s C3 $ s C1 $ s C2 $G s C2 s x z s C2 $ $diff G s C2 , s Q g1I15 d : 2 z s C3 $ s C1 $ s C2 $G s C2 Res1I15 d subs s = 0, D1I15$1 Cg1I15$g

1 z 2 Y 2 g 1 z 1, 2 Y 2 Res1I15 := C 4 4 z 3 z 3 1 z 2 Y 1, 2 4 z 3

K

> D2I15 d diff

g2I15 d

x Q

K

2

z 0 Q Y 1, 1 xz 2

C

K

x Q z 3

Y 2 (33)

1 z 2 Y 2 2 z 3

,s :

2

xz 2

z 2 ln

$diff G s C2 , s

z s C3 $s$ s C2 $G s C2 s x z s C1 $ $diff G s C2 , s Q

z 0 QY 1 g

,s :

s

z s C3 $s$ s C2 $G s C2 Res2I15 d subs s =K1, D2I15$1 Cg2I15$g Res2I15 := K

1 C 4

1 z 2 Y 2 z 1, 3 2 4 z 3

z s C1 $

K

C

2

2 z 0 Q Y 1 z 1, 2

z 0 Q Y 1 z 2, 2

z s C2 $

C

(32)

2

z 1, 0 Q Y 1 xz 2

z 0 Q Y 1 z 1, 2 xz 2

2

: x Q xz 2

z 0 Q ln K C

Y 1

z 0 QY 1 xz 2

D2I2 $ K1 Cg2I2$ Kg 1 2 I3 d subs s = 0, D1I3$1 Cg1I3$g Csubs s =K1, D2I3$1 Cg2I3$g ; I4 d subs s = 0, D1I4$1 Cg1I4$g Csubs s =K1, D2I4$1 Cg2I4$g ;

> I2 d subs s = 0, D1I2$1 Cg1I2$g Csubs s =K1,

(34)

;

D2I5 $ 2 Cg2I5$g 2 ; 6 D2I6 I6 d subs s = 0, D1I6$1 Cg1I6$g Csubs s =K1, $ K1 Cg2I6$ Kg 1 ; 2 D2I7 I7 d subs s = 0, D1I7$1 Cg1I7$g Csubs s =K1, $ K1 Cg2I7$ Kg 1 ; 2 I8 d subs s = 0, D1I8$1 Cg1I8$g Csubs s =K1, D2I8$1 Cg2I8$g ; I9 d subs s = 0, D1I9$1 Cg1I9$g Csubs s =K1, D2I9$1 Cg2I9$g ; I10 d subs s = 0, D1I10$1 Cg1I10$g Csubs s =K1, D2I10$1 Cg2I10$g ; I11 d subs s = 0, D1I11$1 Cg1I11$g Csubs s =K1, D2I11$1 Cg2I11$g ; I12 d subs s = 0, D1I12$1 Cg1I12$g Csubs s =K1, D2I12$1 Cg2I12$g ; D2I13 I13 d subs s = 0, D1I13$1 Cg1I13$g Csubs s =K1, $ K1 Cg2I13$ Kg 1 2 I14 d subs s = 0, D1I14$1 Cg1I14$g Csubs s =K1, D2I14$1 Cg2I14$g ; I15 d subs s = 0, D1I15$1 Cg1I15$g Csubs s =K1, D2I15$1 Cg2I15$g ; x z 1, 2 ln 1 z 1, 2 g 1 z 2, 2 1 Q 1 z 1, 2 z 1, 3 I2 := C C K 2 2 2 z 3 2 2 z 3 z 3 z 3 I5 d subs s = 0, D1I5$1 Cg1I5$g Csubs s =K1,

z 0 Q ln

3 z 1, 2 K 4 z 3 K C

K

xz 2

z 1, 0 Q z 1, 2 xz 2

2

x Q

z 1, 2 2

z 1, 0 Q ln C

1 C 2

x Q

K

xz 2

2

x Q

z 0 Q ln

C

xz 2 1 z 0 Q z 2, 2 2 2 xz 2

C

z 0 Q z 1, 2 xz 2

2

3

z 0 Q xz 2

z 0 Qg 1 1 z 2, 0 Q C 2 xz 2 xz 2

1 z 2 z 1, 3 g 1 z 1, 2 z 1, 3 I3 := C 2 2 2 2 z 3 z 3

1 C 2

z 2 ln

x Q z 3

z 1, 3 K

2

z 2 z 1, 3 z 3

z 0 Q z 1, 2 g z 1, 0 Q z 1, 2 3 z 2 z 1, 3 1 z 2 z 2, 3 C K K 2 2 2 2 4 2 z 3 z 3 xz 2 xz 2 x 2 z 0 Q ln z 1, 2 2 z 0 Q z 1, 2 z 0 Q z 2, 2 Q K C K 2 3 2 xz 2 xz 2 xz 2 x z 2 ln z 2 g z 1, 2 1 1 1 Q 1 z 2 z 1, 3 1 z 2 I4 := C C K K 2 4 z 3 4 z 3 4 4 2 z 3 z 3 z 3 K

K

;

z 0 Qg xz 2

K

z 1, 0 Q xz 2

z 0 Q ln K

xz 2

x Q

C

z 0 Q z 1, 2 xz 2

2

C

z 0 Q xz 2

3

2

1 z 2, 2 g 1 z 3, 2 I5 := C 2 2 z 3 z 3 3 z 2, 2 K 4 z 3

K

C

C

I6 :=

2

x Q

z 1, 2

2 z 0 Q z 1, 2 z 2, 2 3

xz 2

2 z 0 Q z 1, 2

K

4

xz 2

z 2, 0 Q z 1, 2 xz 2

K

C

2

x Q

C

xz 2

xz 2 z 0 Qg 2

K

xz 2

z 1, 0 Q ln

3

K

xz 2 z 1, 0 Q z 2, 2 xz 2

2

K

z 3

K

3

2 z 0 Q ln K

2

x Q

xz 2

z 2, 2 2

3

xz 2 2

2 z 1, 0 Q z 1, 2 3

xz 2

x Q

C

xz 2

1 z 0 Q z 3, 2 2 3 xz 2

2

3 z 1, 2 z 1, 3 2 4 z 3

z 1, 2

3 z 0 Q z 1, 2 z 2, 2 xz 2

1 3

x Q

xz 2 x Q

z 0 Q ln

K

2

1 C 2

C

C

C

z 3

C x Q 2

2

x Q

2

z 1, 2 K

2

2 z 1, 0 Q z 1, 2

1 z 0 Q z 3, 2 2 2 xz 2 z 2, 2

2

z 0 Q z 1, 2 g 1 2

z 1, 3

1 z 1, 2 z 2, 3 2 2 z 3

xz 2

xz 2

x Q

z 1, 2 ln

1 2

z 0 Q ln

z 1, 0 Q z 2, 2 1 z 2, 0 Q z 1, 2 C 2 2 2 xz 2 xz 2 x z 1, 0 Q ln z 1, 2 z 0 Q ln Q C C 2 xz 2 xz 3

C

2

z 2, 0 Q ln

C

K

z 0 Q ln

2 z 0 Q z 1, 2

3

xz 2

3

xz 2 z 1, 2

2

2

x Q

1 z 1, 2 z 1, 3 g 1 z 2, 2 z 1, 3 C 2 2 2 2 z 3 z 3 z 1, 2 z 1, 3

x Q

2 z 1, 0 Q ln

1 z 2, 2 z 1, 3 2 2 z 3 x 2 z 0 Q ln z 1, 2 Q K

z 3

C

2

xz 2

2 z 0 Q ln K

1 2

2 z 1, 0 Q 1 z 3, 0 Q K K K 3 xz 2 xz 2

z 0 Q ln C

C

x Q

z 2, 2 ln

C

xz 2 C

3

z 0 Q z 1, 2 xz 2

3 z 0 Q z 1, 2 xz 2

2

4

3

2

1 z 1, 2 g 1 z 2, 2 I7 := C 4 4 z 3 z 3

C

z 0 Q ln

x Q

1 z 1, 2 K 2 z 3 K

K

K

2

xz 2

1 z 0 Q z 2, 2 2 2 xz 2 x Q

z 0 Q ln

1 4

K

1 C 2

xz 2

1 z 1, 2 z 1, 3 2 4 z 3 z 3 x z 1, 2 z 1, 0 Q ln z 1, 0 Q z 1, 2 Q C K 2 xz 2 xz 2

z 1, 0 Q xz 2

2z 0 Q

C

z 0 Q ln

xz 2 x Q

K K

I9 :=

z 2 z 2, 3 z 1, 3 z 3

2

xz 2

2

z 0 Q z 1, 2

C

xz 2

x Q

z 2 ln

1 C 2

C

3

z 3

z 0 Qg 1 xz 2

z 2, 3 2

K

2 2

g

C

1 z 1, 2 z 1, 3 3 2 z 3

3

3 z 2 z 1, 3 K 4 2 z 3

3 z 2 z 1, 3 K 3 4 z 3 x 2 z 0 Q ln z 1, 0 Q z 1, 2 Q K K 3 xz 2 xz 2

2

C

2

C

x Q

z 2 ln

1 2

z 3 z 3

3

K

3

z 0 Q z 1, 2 xz 2

2

C

3

2

z 1, 3

z 2 z 2, 3 z 1, 3

z 1, 2

3

3 z 0 Q z 1, 2 xz 2

3

4

2 z 0 Q z 1, 2 z 2, 2 xz 2

3

1 z 2 z 1, 3 g 1 z 1, 2 z 1, 3 I10 := C 2 2 4 4 z 3 z 3 K

z 0 Q z 1, 2 1 z 2, 0 Q C 2 2 xz 2 xz 2

z 0 Q z 3, 2

1 z 2 z 1, 3 3 2 z 3

K

C

z 0 Q z 2, 2 g 3 z 2 z 2, 3 1 z 2 z 3, 3 C K 2 2 2 4 2 z 3 z 3 xz 2 x z 0 Q ln z 2, 2 2 z 0 Q z 1, 2 z 2, 2 Q K C 2 3 xz 2 xz 2

3

z 1, 0 Q z 2, 2 xz 2

K

2

xz 2

1 z 2 z 2, 3 g 1 z 1, 2 z 2, 3 I8 := C 2 2 2 2 z 3 z 3 K

x Q

z 1, 2 ln

1 z 2 z 1, 3 3 2 z 3

2

K

1 z 2 z 1, 3 2 2 z 3

1 C 4 C

x Q

z 2 ln

z 3

1 z 2 z 2, 3 2 4 z 3

z 1, 3 2

K

z 0 Q z 1, 2 g xz 2

2

2

g

K C

z 0 Q z 1, 2

K

2

xz 2

K

2

xz 2

K

I12 :=

K

xz 2

xz 2

x Q

C I14 :=

xz 2

K

K

z 1, 0 Q Y 1, 1 xz 2

x Q

xz 2

K

xz 2

K

xz 2

C

C

1 z 2 Y 1, 2 2 z 3

z 1, 0 Q Y 1 xz 2

Y 2

2

C

1 z 2, 0 Q Y 1 2 xz 2

z 0 QY 1 xz 2

2

x Q xz 2

z 0 Q ln

xz 2

3 z 1, 2 Y 2 4 z 3

3

z 0 Q Y 1, 1 z 1, 2

Y 1

2z 0 Q

2

x Q z 3

z 1, 2 ln

z 0 Q Y 1 z 1, 2

xz 2

5 z 2 16 z 3

z 0 Q Y 1 z 1, 2

1 z 1, 2 Y 2 z 1, 3 2 2 z 3

C

K

C

K

xz 2

1 2

C

1 z 0 Q Y 2, 1 2 xz 2

2

2

z 0 QY 1 g

C

xz 2

C

z 1, 0 Q Y 1 z 1, 2 xz 2

K

z 0 Q Y 1, 1

2

C

z 0 Q z 1, 2

C

xz 2 x z 2 ln Y 2 1 Q C 2 z 3

3 z 2 Y 2 4 z 3

Y 1 z 1, 2

xz 2

z 1, 0 Q ln C

x Q

1 z 2 z 1, 3 2 8 z 3

K

z 3

1 z 1, 2 Y 2 g 1 z 2, 2 Y 2 C 2 2 z 3 z 3

K

K

K

x Q

z 2 ln

1 z 2 Y 2 g 1 z 1, 2 Y 2 C 2 2 z 3 z 3

z 0 Q ln

C

1 C 8

K

xz 2

1 z 1, 2 Y 1, 2 2 z 3

3

xz 2

2

z 0 Q ln

z 1, 0 Q

1 z 2 Y 2 z 1, 3 2 2 z 3 x z 0 Q ln Y 1 Q K xz 2

C

C

2

2

2 z 0 Q z 1, 2

z 0 Q z 2, 2

K

I13 :=

z 1, 2

xz 2

1 z 2 g 1 z 1, 2 I11 := C 8 z 3 8 z 3 z 0 Qg

x Q

z 0 Q ln

z 1, 0 Q z 1, 2

Y 1, 1

z 0 QY 1 g 1 xz 2 1 z 2 Y 2 z 1, 3 g 1 z 1, 2 Y 2 z 1, 3 C 2 2 2 2 z 3 z 3

K

1 z 0 Q Y 1 z 2, 2 2 2 xz 2 1 C 2

x Q xz 2

z 0 Q ln

2

Y 1

1 C 2 K

K

C

z 2 ln

x Q

Y 2 z 1, 3

z 3

2

3 z 2 Y 2 z 1, 3 2 4 z 3

xz 2

3

2

K

1 z 2 Y 2 z 1, 3 2 4 z 3 x z 0 Q ln Y 1 Q K xz 2 >

3

z 0 Q Y 1 z 2, 2 xz 2

1 z 2 Y 2 g 1 z 1, 2 Y 2 I15 := C 4 4 z 3 z 3 K

z 3

2

z 0 Q Y 1 z 1, 2 g 1 z 2 Y 2 z 2, 3 K 2 2 2 z 3 xz 2 x z 0 Q ln Y 1 z 1, 2 z 0 Q Y 1, 1 z 1, 2 Q K K 2 2 xz 2 xz 2

2

2 z 0 Q Y 1 z 1, 2

K

z 2 Y 2 z 1, 3

C

z 1, 0 Q Y 1 z 1, 2 xz 2

1 z 2 Y 1, 2 z 1, 3 C 2 2 z 3

K

K

1 C 4

1 z 2 Y 2 2 z 3 z 0 Q Y 1, 1 xz 2

2

z 2 ln

K

x Q z 3

Y 2 C

z 0 QY 1 g

C

xz 2

K

z 1, 0 Q Y 1

z 0 Q Y 1 z 1, 2 xz 2

2

1 z 2 Y 1, 2 4 z 3 xz 2 C

z 0 QY 1 xz 2

(35)