>	restart:grtw();

 

 

 

 

 

 

	(1)

 

>	l:=1:grload(AdS,`/home/grumil/projects/BHfreeCCTMG/AdS3lccx.mpl`):

 

 

 

 

 

 

 

 

 

Calculated ds for AdS (0.000000 sec.)
	(2)

 

>	hdp:=-h-hp:

 

>	bhdp:=-bh-bhp:

 

>	grload(log1,`/home/grumil/projects/BHfreeCCTMG/Logasymptoticsimple.mpl`):

 

 

 

 

 

 

 

 

 

Calculated ds for log1 (0.000000 sec.)
	(3)

 

>	grdef(`Psi1{a b}:=g<2>{a b}`);

 

Created definition for Psi1(dn,dn)

 

>	grcalc(2=log1,Psi1(dn,dn));

 

 

Calculated Psi1(dn,dn) for log1 (0.004000 sec.)
	(4)

 

>	grmetric(AdS);

 

Default metric is now AdS.

 

>	grdef(`Psi1U{a ^b}:=Psi1{a c}*g{^c ^b}`);

 

Created definition for Psi1U(dn,up)

 

>	grdef(`Psi1UU{^a ^b}:=Psi1U{c ^b}*g{^c ^a}`);

 

Created definition for Psi1UU(up,up)

 

>	grdef(`deChr1{^a b c}:=g{^a ^d}*(Psi1{d b ;c}+Psi1{d c ;b}-Psi1{b c ;d})/2`);

 

Created a definition for Psi1(dn,dn,cdn) Created definition for deChr1(up,dn,dn)

 

>	grload(log2,`/home/grumil/projects/BHfreeCCTMG/Logasymptoticprimesimple.mpl`):

 

 

 

 

 

 

 

 

 

Calculated ds for log2 (0.000000 sec.)
	(5)

 

>	grdef(`Psi2{a b}:=g<3>{a b}`);

 

Created definition for Psi2(dn,dn)

 

>	grcalc(3=log2,Psi2(dn,dn));

 

 

Calculated Psi2(dn,dn) for log2 (0.000000 sec.)
	(6)

 

>	grmetric(AdS);

 

Default metric is now AdS.

 

>	grdef(`Psi2U{a ^b}:=Psi2{a c}*g{^c ^b}`);

 

Created definition for Psi2U(dn,up)

 

>	grdef(`Psi2UU{^a ^b}:=Psi2U{c ^b}*g{^c ^a}`);

 

Created definition for Psi2UU(up,up)

 

>	grdef(`deChr2{^a b c}:=g{^a ^d}*(Psi2{d b ;c}+Psi2{d c ;b}-Psi2{b c ;d})/2`);

 

Created a definition for Psi2(dn,dn,cdn)

 

Created definition for deChr2(up,dn,dn)

 

>	grload(right,`/home/grumil/projects/BHfreeCCTMG/Logasymptoticdoubleprimesimple.mpl`):

 

 

 

 

 

 

 

 

 

Calculated ds for right (0.000000 sec.)
	(7)

 

>	grdef(`PsiR{a b}:=g<4>{a b}`);

 

Created definition for PsiR(dn,dn)

 

>	grcalc(4=right,PsiR(dn,dn));

 

 

Calculated PsiR(dn,dn) for right (0.000000 sec.)
	(8)

 

>	grmetric(AdS);

 

Default metric is now AdS.

 

>	grdef(`PsiRU{a ^b}:=PsiR{a c}*g{^c ^b}`);

 

Created definition for PsiRU(dn,up)

 

>	grdef(`PsiRUU{^a ^b}:=PsiRU{c ^b}*g{^c ^a}`);

 

Created definition for PsiRUU(up,up)

 

>	grdef(`deChrR{^a b c}:=g{^a ^d}*(PsiR{d b ;c}+PsiR{d c ;b}-PsiR{b c ;d})/2`);

 

Created a definition for PsiR(dn,dn,cdn) Created definition for deChrR(up,dn,dn)

 

>	grload(left1,`/home/grumil/projects/BHfreeCCTMG/Lasymptoticsimple.mpl`):

 

 

 

 

 

 

 

 

 

Calculated ds for left1 (0.000000 sec.)
	(9)

 

>	grdef(`PsiL1{a b}:=g<5>{a b}`);

 

Created definition for PsiL1(dn,dn)

 

>	grcalc(5=left1,PsiL1(dn,dn));

 

 

Calculated PsiL1(dn,dn) for left1 (0.000000 sec.)
	(10)

 

>	grmetric(AdS);

 

Default metric is now AdS.

 

>	grdef(`PsiL1U{a ^b}:=PsiL1{a c}*g{^c ^b}`);

 

Created definition for PsiL1U(dn,up)

 

>	grdef(`PsiL1UU{^a ^b}:=PsiL1U{c ^b}*g{^c ^a}`);

 

Created definition for PsiL1UU(up,up)

 

>	grload(left2,`/home/grumil/projects/BHfreeCCTMG/Lasymptoticprimesimple.mpl`):

 

 

 

 

 

 

 

 

 

Calculated ds for left2 (0.000000 sec.)
	(11)

 

>	grdef(`PsiL2{a b}:=g<6>{a b}`);

 

Created definition for PsiL2(dn,dn)

 

>	grcalc(6=left2,PsiL2(dn,dn));

 

 

Calculated PsiL2(dn,dn) for left2 (0.000000 sec.)
	(12)

 

>	grmetric(AdS);

 

Default metric is now AdS.

 

>	grdef(`PsiL2U{a ^b}:=PsiL2{a c}*g{^c ^b}`);

 

Created definition for PsiL2U(dn,up)

 

>	grdef(`PsiL2UU{^a ^b}:=PsiL2U{c ^b}*g{^c ^a}`);

 

Created definition for PsiL2UU(up,up)

 

>	grload(left,`/home/grumil/projects/BHfreeCCTMG/Lasymptoticdoubleprimesimple.mpl`):

 

 

 

 

 

 

 

 

 

Calculated ds for left (0.000000 sec.)
	(13)

 

>	grdef(`PsiL{a b}:=g<7>{a b}`);

 

Created definition for PsiL(dn,dn)

 

>	grcalc(7=left,PsiL(dn,dn));

 

 

Calculated PsiL(dn,dn) for left (0.000000 sec.)
	(14)

 

>	grmetric(AdS);

 

Default metric is now AdS.

 

>	grdef(`PsiLU{a ^b}:=PsiL{a c}*g{^c ^b}`);

 

Created definition for PsiLU(dn,up)

 

>	grdef(`PsiLUU{^a ^b}:=PsiLU{c ^b}*g{^c ^a}`);

 

Created definition for PsiLUU(up,up)

 

>	grdef(`deRiem1{^a b c d}:=deChr1{^a b d ;c}-deChr1{^a b c ;d}`);

 

Created a definition for deChr1(up,dn,dn,cdn)

 

Created definition for deRiem1(up,dn,dn,dn)

 

>	grdef(`deRiem2{^a b c d}:=deChr2{^a b d ;c}-deChr2{^a b c ;d}`);

 

Created a definition for deChr2(up,dn,dn,cdn)

 

Created definition for deRiem2(up,dn,dn,dn)

 

>	grdef(`deRiemR{^a b c d}:=deChrR{^a b d ;c}-deChrR{^a b c ;d}`);

 

Created a definition for deChrR(up,dn,dn,cdn) Created definition for deRiemR(up,dn,dn,dn)

 

>	grdef(`deRic12{(a b)}:=Psi1U{c ^d}*deRiem2{^c a b d}+(2*Psi1U{a ^c ;d}*Psi2{c b ;e}*g{^d ^e}-2*Psi1U{a ^c ;d}*Psi2U{b ^d ;c}+Psi1UU{^c ^d ;a}*Psi2{c d ;b})/4+Psi2U{c ^d}*deRiem1{^c a b d}+(2*Psi2U{a ^c ;d}*Psi1{c b ;e}*g{^d ^e}-2*Psi2U{a ^c ;d}*Psi1U{b ^d ;c}+Psi2UU{^c ^d ;a}*Psi1{c d ;b})/4`);

 

Created a definition for Psi1U(dn,up,cdn) Created a definition for Psi2U(dn,up,cdn)

 

Created a definition for Psi1UU(up,up,cdn) Created a definition for Psi2UU(up,up,cdn) Created definition for deRic12(dn,dn)

 

>	grdef(`De12{(a b)}:=(-(Psi2U{a ^c}*PsiL1{c b})+(PsiL1{c d}*LevC{a ^c ^e}*deChr2{^d b e})-(Psi1U{a ^c}*PsiL2{c b})+(PsiL2{c d}*LevC{a ^c ^e}*deChr1{^d b e}))`);

 

Created definition for LevC(dn,up,up)

 

Created definition for De12(dn,dn)

 

>

grcalcalter(detg,simplify);grcalcalter(g(up,up),simplify);grcalcalter(Psi1(dn,dn),simplify);grcalcalter(Psi1U(dn,up),simplify);grcalcalter(Psi1UU(up,up),simplify);grcalcalter(Psi2(dn,dn),simplify);grcalcalter(Psi2U(dn,up),simplify);grcalcalter(Psi2UU(up,up),simplify);grcalcalter(PsiL1(dn,dn),simplify);grcalcalter(PsiL1U(dn,up),simplify);grcalcalter(PsiL1UU(up,up),simplify);grcalcalter(PsiL2(dn,dn),simplify);grcalcalter(PsiL2U(dn,up),simplify);grcalcalter(PsiL2UU(up,up),simplify);grcalcalter(Chr(dn,dn,dn),simplify);grcalcalter(Chr(dn,dn,up),simplify);grcalcalter(deChr1(up,dn,dn),simplify);grcalcalter(deChr2(up,dn,dn),simplify);grcalcalter(deChrR(up,dn,dn),simplify);grcalcalter(De12(dn,dn),simplify);

 

 

Simplification will be applied during calculation.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Applying routine simplify to object detg Calculated detg for AdS (0.000000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object g(up,up) Calculated g(up,up) for AdS (0.000000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object Psi1(dn,dn) Calculated Psi1(dn,dn) for AdS (0.020000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object Psi1U(dn,up) Calculated Psi1U(dn,up) for AdS (0.032000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object Psi1UU(up,up) Calculated Psi1UU(up,up) for AdS (0.032000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object Psi2(dn,dn) Calculated Psi2(dn,dn) for AdS (0.012000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object Psi2U(dn,up) Calculated Psi2U(dn,up) for AdS (0.020000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object Psi2UU(up,up) Calculated Psi2UU(up,up) for AdS (0.032000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object PsiL1(dn,dn) Calculated PsiL1(dn,dn) for AdS (0.004000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object PsiL1U(dn,up) Calculated PsiL1U(dn,up) for AdS (0.012000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object PsiL1UU(up,up) Calculated PsiL1UU(up,up) for AdS (0.016000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object PsiL2(dn,dn) Calculated PsiL2(dn,dn) for AdS (0.004000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object PsiL2U(dn,up) Calculated PsiL2U(dn,up) for AdS (0.012000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object PsiL2UU(up,up) Calculated PsiL2UU(up,up) for AdS (0.016000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object g(dn,dn,pdn) Calculated g(dn,dn,pdn) for AdS (0.000000 sec.) Applying routine simplify to object Chr(dn,dn,dn) Calculated Chr(dn,dn,dn) for AdS (0.000000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object Chr(dn,dn,up) Calculated Chr(dn,dn,up) for AdS (0.004000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object Psi1(dn,dn,cdn) Calculated Psi1(dn,dn,cdn) for AdS (0.136000 sec.) Applying routine simplify to object deChr1(up,dn,dn) Calculated deChr1(up,dn,dn) for AdS (0.260000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object Psi2(dn,dn,cdn) Calculated Psi2(dn,dn,cdn) for AdS (0.132000 sec.) Applying routine simplify to object deChr2(up,dn,dn) Calculated deChr2(up,dn,dn) for AdS (0.264000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object PsiR(dn,dn) Calculated PsiR(dn,dn) for AdS (0.012000 sec.) Applying routine simplify to object PsiR(dn,dn,cdn) Calculated PsiR(dn,dn,cdn) for AdS (0.352000 sec.) Applying routine simplify to object deChrR(up,dn,dn)
Calculated deChrR(up,dn,dn) for AdS (1.016000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object LevC(up,up,up) Calculated LevC(up,up,up) for AdS (0.000000 sec.) Applying routine simplify to object LevC(dn,up,up) Calculated LevC(dn,up,up) for AdS (0.000000 sec.) Applying routine simplify to object De12(dn,dn)
Calculated De12(dn,dn) for AdS (1.468000 sec.)
	(15)

 

>	grcalcalter(deRiem1(up,dn,dn,dn),simplify);grcalcalter(deRiem2(up,dn,dn,dn),simplify);grcalcalter(deRiemR(up,dn,dn,dn),simplify);grcalcalter(deRic12(dn,dn),simplify);

 

 

Simplification will be applied during calculation. Applying routine simplify to object deChr1(up,dn,dn,cdn)

 

Calculated deChr1(up,dn,dn,cdn) for AdS (1.972000 sec.) Applying routine simplify to object deRiem1(up,dn,dn,dn)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Calculated deRiem1(up,dn,dn,dn) for AdS (1.336000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object deChr2(up,dn,dn,cdn)
Calculated deChr2(up,dn,dn,cdn) for AdS (1.996000 sec.) Applying routine simplify to object deRiem2(up,dn,dn,dn)
Calculated deRiem2(up,dn,dn,dn) for AdS (1.504000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object deChrR(up,dn,dn,cdn)
Calculated deChrR(up,dn,dn,cdn) for AdS (18.525000 sec.) Applying routine simplify to object deRiemR(up,dn,dn,dn)
Calculated deRiemR(up,dn,dn,dn) for AdS (13.461000 sec.)
Simplification will be applied during calculation. Applying routine simplify to object Psi1U(dn,up,cdn)
Calculated Psi1U(dn,up,cdn) for AdS (0.264000 sec.) Applying routine simplify to object Psi2U(dn,up,cdn) Calculated Psi2U(dn,up,cdn) for AdS (0.260000 sec.) Applying routine simplify to object Psi1UU(up,up,cdn)
Calculated Psi1UU(up,up,cdn) for AdS (0.208000 sec.) Applying routine simplify to object Psi2UU(up,up,cdn)
Calculated Psi2UU(up,up,cdn) for AdS (0.228000 sec.) Applying routine simplify to object deRic12(dn,dn)
Calculated deRic12(dn,dn) for AdS (39.939000 sec.)
	(16)

 

>

 

>	grdef(`Corpart1:=2*c*PsiLUU{^a ^b}*deRic12{(a b)}`);

 

Created definition for Corpart1

 

>	grdef(`Corpart2:=2*c*PsiRUU{^a ^b}*De12{(a b)}`);

 

Created definition for Corpart2

 

>	grcalcalter(Corpart1,simplify);

 

 

Simplification will be applied during calculation. Applying routine simplify to object PsiL(dn,dn) Calculated PsiL(dn,dn) for AdS (0.008000 sec.) Applying routine simplify to object PsiLU(dn,up) Calculated PsiLU(dn,up) for AdS (0.016000 sec.) Applying routine simplify to object PsiLUU(up,up)

 

Calculated PsiLUU(up,up) for AdS (0.024000 sec.) Applying routine simplify to object Corpart1

 

Calculated Corpart1 for AdS (434.503000 sec.)
	(17)

 

>	grcalcalter(Corpart2,simplify);

 

 

Simplification will be applied during calculation. Applying routine simplify to object PsiRU(dn,up)

 

Calculated PsiRU(dn,up) for AdS (0.032000 sec.) Applying routine simplify to object PsiRUU(up,up) Calculated PsiRUU(up,up) for AdS (0.172000 sec.) Applying routine simplify to object Corpart2

 

Calculated Corpart2 for AdS (63.168000 sec.)
	(18)

 

>	integrandCorpart1:=series(simplify(subs(u=t+phi,(subs(v=t-phi,(grcomponent(Corpart1))*2*Pi/8)))),xx=infinity,10);

 

(19)

 

>	integrandCorpart2:=series(simplify(subs(u=t+phi,(subs(v=t-phi,(grcomponent(Corpart2))*2*Pi/8)))),xx=infinity,10);

 

(20)

 

>	part1:=collect(collect(collect(series(subs(h=a*h,subs(bh=a*bh,subs(hp=a*hp,subs(bhp=a*bhp,integrandCorpart1)))),a=infinity,5),t),log(xx)),a);

 

(21)

 

>	part2:=collect(collect(collect(series(subs(h=a*h,subs(bh=a*bh,subs(hp=a*hp,subs(bhp=a*bhp,integrandCorpart2)))),a=infinity,5),t),log(xx)),a);

 

(22)

 

>	collect(collect(collect(simplify(part1+part2),t),log(xx)),a);

 

(23)

 

>

a4logxsq:=simplify(-2*(464*c^3*Pi*bh*h^4*bhp*hp+304*c^3*Pi*bh*h^2*hp^3*bhp+208*c^3*Pi*h^3*hp^2*bhp^2+304*c^3*Pi*bh*hp^2*bhp*h^3+208*c^3*Pi*h^2*bh^2*hp^3+464*c^3*Pi*bhp*hp^4*bh*h+96*c^3*Pi*h^5*bhp^2+96*c^3*Pi*hp^5*bh^2+192*c^3*Pi*h^5*bh*bhp+192*c^3*Pi*hp^5*bhp*bh+272*c^3*Pi*h^4*hp*bhp^2+272*c^3*Pi*h*hp^4*bh^2)/bh/bhp/(bh+bhp));

 

(24)

 

>	a4logxt:=simplify(-((2*(-(64*I)*c^3*Pi*bh*hp^2*h^3*bhp-(64*I)*c^3*Pi*bh^2*hp^3*h^2-(64*I)*c^3*Pi*h^2*hp^3*bh*bhp-(64*I)*c^3*Pi*bhp^2*hp^2*h^3))*t/((bh+bhp)*bh*bhp*xx^2))/bh/bhp/(bh+bhp));

 

(25)

 

>

a4tsq:=simplify(-((2*(384*c^3*Pi*hp^5*bh^2+384*c^3*Pi*h^5*bhp^2+1344*c^3*Pi*bh*hp^2*bhp*h^3+1344*c^3*Pi*bh*h^2*hp^3*bhp+960*c^3*Pi*h^3*hp^2*bhp^2+1856*c^3*Pi*bh*h^4*bhp*hp+1088*c^3*Pi*h^4*hp*bhp^2+768*c^3*Pi*hp^5*bhp*bh+768*c^3*Pi*h^5*bh*bhp+960*c^3*Pi*h^2*bh^2*hp^3+1088*c^3*Pi*h*hp^4*bh^2+1856*c^3*Pi*bhp*hp^4*bh*h))*t^2/((bh+bhp)*bh*bhp*xx^2)));

 

(26)

 

>

a4t:=simplify(-((2*(-(288*I)*c^3*Pi*h^5*bh*bhp-(800*I)*c^3*Pi*bh^2*hp^3*h^2-(384*I)*c^3*Pi*bh*h^5*bhp*ln(-a^2*h*bh)-(672*I)*c^3*Pi*bh*hp^2*h^3*bhp-(896*I)*c^3*Pi*h^3*hp^2*bhp*bh*ln(-a^2*h*bh)-(800*I)*c^3*Pi*bhp^2*hp^2*h^3-(384*I)*c^3*Pi*hp^5*ln(-(h+hp)*(bh+bhp)*a^2)*bh*bhp-(288*I)*c^3*Pi*hp^5*bhp*bh-(128*I)*c^3*Pi*h^5*bhp^2-(128*I)*c^3*Pi*hp^5*bh^2-(1088*I)*c^3*Pi*hp^4*bh^2*h*ln(-a^2*hp*bhp)-(384*I)*c^3*Pi*hp^5*bh^2*ln(-a^2*hp*bhp)-(864*I)*c^3*Pi*bhp*h*bh*hp^4-(672*I)*c^3*Pi*h^2*hp^3*bh*bhp-(1088*I)*c^3*Pi*bh*h^4*hp*bhp*ln(-a^2*h*bh)-(384*I)*c^3*Pi*bhp*hp^5*bh*ln(-a^2*hp*bhp)-(640*I)*c^3*Pi*bh^2*hp^4*h-(864*I)*c^3*Pi*h^4*hp*bh*bhp-(384*I)*c^3*Pi*h^5*bhp^2*ln(-a^2*h*bh)-(1088*I)*c^3*Pi*h^4*bhp^2*hp*ln(-a^2*h*bh)-(768*I)*c^3*Pi*h^4*hp*ln(-(h+hp)*(bh+bhp)*a^2)*bh*bhp-(384*I)*c^3*Pi*h^5*ln(-(h+hp)*(bh+bhp)*a^2)*bh*bhp-(896*I)*c^3*Pi*bhp*hp^3*h^2*ln(-a^2*hp*bhp)*bh-(768*I)*c^3*Pi*hp^4*ln(-(h+hp)*(bh+bhp)*a^2)*h*bhp*bh-(640*I)*c^3*Pi*bhp^2*hp*h^4-(384*I)*c^3*Pi*h^2*hp^3*ln(-(h+hp)*(bh+bhp)*a^2)*bhp*bh-(896*I)*c^3*Pi*bh^2*hp^3*h^2*ln(-a^2*hp*bhp)-(896*I)*c^3*Pi*bhp^2*h^3*hp^2*ln(-a^2*h*bh)-(1088*I)*c^3*Pi*bhp*h*hp^4*bh*ln(-a^2*hp*bhp)-(384*I)*c^3*Pi*h^3*hp^2*ln(-(h+hp)*(bh+bhp)*a^2)*bhp*bh))*t/((bh+bhp)*bh*bhp*xx^2)));

 

(27)

 

>

a4logx:=simplify(-((2*(-320*c^3*Pi*h^5*bhp^2-320*c^3*Pi*hp^5*bh^2-1488*c^3*Pi*bh*h^4*bhp*hp-1040*c^3*Pi*bh*h^2*hp^3*bhp-592*c^3*Pi*h^3*hp^2*bhp^2-1040*c^3*Pi*bh*hp^2*bhp*h^3-592*c^3*Pi*h^2*bh^2*hp^3-1488*c^3*Pi*bhp*hp^4*bh*h-624*c^3*Pi*h^5*bh*bhp-624*c^3*Pi*hp^5*bhp*bh-832*c^3*Pi*h^4*hp*bhp^2-832*c^3*Pi*h*hp^4*bh^2-544*c^3*Pi*bh*h^4*hp*bhp*ln(-a^2*h*bh)-544*c^3*Pi*hp^4*bh^2*h*ln(-a^2*hp*bhp)-448*c^3*Pi*bh^2*hp^3*h^2*ln(-a^2*hp*bhp)-192*c^3*Pi*hp^5*bh^2*ln(-a^2*hp*bhp)-192*c^3*Pi*bh*h^5*bhp*ln(-a^2*h*bh)-384*c^3*Pi*hp^4*ln(-(h+hp)*(bh+bhp)*a^2)*h*bhp*bh-192*c^3*Pi*h^5*ln(-(h+hp)*(bh+bhp)*a^2)*bh*bhp-192*c^3*Pi*h^2*hp^3*ln(-(h+hp)*(bh+bhp)*a^2)*bhp*bh-544*c^3*Pi*h^4*bhp^2*hp*ln(-a^2*h*bh)-448*c^3*Pi*bhp*hp^3*h^2*ln(-a^2*hp*bhp)*bh-192*c^3*Pi*bhp*hp^5*bh*ln(-a^2*hp*bhp)-192*c^3*Pi*h^5*bhp^2*ln(-a^2*h*bh)-192*c^3*Pi*hp^5*ln(-(h+hp)*(bh+bhp)*a^2)*bh*bhp-384*c^3*Pi*h^4*hp*ln(-(h+hp)*(bh+bhp)*a^2)*bh*bhp-192*c^3*Pi*h^3*hp^2*ln(-(h+hp)*(bh+bhp)*a^2)*bhp*bh-544*c^3*Pi*bhp*h*hp^4*bh*ln(-a^2*hp*bhp)-448*c^3*Pi*bhp^2*h^3*hp^2*ln(-a^2*h*bh)-448*c^3*Pi*h^3*hp^2*bhp*bh*ln(-a^2*h*bh)))/((bh+bhp)*bh*bhp*xx^2)));

 

(28)

 

>

a4rest:=collect(collect(collect(simplify(-((2*(288*c^3*Pi*h^5*bhp^2+288*c^3*Pi*hp^5*bh^2+1280*c^3*Pi*bh*h^4*bhp*hp+1184*c^3*Pi*bh*h^2*hp^3*bhp+672*c^3*Pi*h^3*hp^2*bhp^2+1184*c^3*Pi*bh*hp^2*bhp*h^3+672*c^3*Pi*h^2*bh^2*hp^3+1280*c^3*Pi*bhp*hp^4*bh*h+512*c^3*Pi*h^5*bh*bhp+512*c^3*Pi*hp^5*bhp*bh+736*c^3*Pi*h^4*hp*bhp^2+736*c^3*Pi*h*hp^4*bh^2+512*c^3*Pi*bh*h^4*hp*bhp*ln(-a^2*h*bh)+512*c^3*Pi*hp^4*bh^2*h*ln(-a^2*hp*bhp)+192*c^3*Pi*bh^2*hp^3*h^2*ln(-a^2*hp*bhp)+256*c^3*Pi*hp^5*bh^2*ln(-a^2*hp*bhp)+256*c^3*Pi*bh*h^5*bhp*ln(-a^2*h*bh)+544*c^3*Pi*hp^4*ln(-(h+hp)*(bh+bhp)*a^2)*h*bhp*bh+224*c^3*Pi*h^5*ln(-(h+hp)*(bh+bhp)*a^2)*bh*bhp+512*c^3*Pi*h^2*hp^3*ln(-(h+hp)*(bh+bhp)*a^2)*bhp*bh+512*c^3*Pi*h^4*bhp^2*hp*ln(-a^2*h*bh)+192*c^3*Pi*bhp*hp^3*h^2*ln(-a^2*hp*bhp)*bh+256*c^3*Pi*bhp*hp^5*bh*ln(-a^2*hp*bhp)+256*c^3*Pi*h^5*bhp^2*ln(-a^2*h*bh)+224*c^3*Pi*hp^5*ln(-(h+hp)*(bh+bhp)*a^2)*bh*bhp+544*c^3*Pi*h^4*hp*ln(-(h+hp)*(bh+bhp)*a^2)*bh*bhp+512*c^3*Pi*h^3*hp^2*ln(-(h+hp)*(bh+bhp)*a^2)*bhp*bh+512*c^3*Pi*bhp*h*hp^4*bh*ln(-a^2*hp*bhp)+192*c^3*Pi*bhp^2*h^3*hp^2*ln(-a^2*h*bh)+192*c^3*Pi*h^3*hp^2*bhp*bh*ln(-a^2*h*bh)))/((bh+bhp)*bh*bhp*xx^2))),log(-a^2*h*bh)),log(-a^2*hp*bhp)),log(-(h+hp)*(bh+bhp)*a^2));

 

(29)

 

>	a4logweightdoubleprime:=simplify(-64*c^3*Pi*(17*bhp*hp^4*bh*h+7*h^5*bh*bhp+16*bh*h^2*hp^3*bhp+16*bh*hp^2*bhp*h^3+17*bh*h^4*bhp*hp+7*hp^5*bhp*bh)/bh/bhp/(bh+bhp));

 

(30)

 

>	a4logweightprime:=simplify(-64*c^3*Pi*(6*h^2*bh^2*hp^3+16*bhp*hp^4*bh*h+8*hp^5*bhp*bh+16*h*hp^4*bh^2+8*hp^5*bh^2+6*bh*h^2*hp^3*bhp)/bh/bhp/(bh+bhp));

 

(31)

 

>	a4logweight:=simplify(-64*c^3*Pi*(8*h^5*bhp^2+16*h^4*hp*bhp^2+6*h^3*hp^2*bhp^2+16*bh*h^4*bhp*hp+8*h^5*bh*bhp+6*bh*hp^2*bhp*h^3)/bh/bhp/(bh+bhp));

 

(32)

 

>	a4rat:=simplify(-(64*c^3*Pi*(23*h^4*hp*bhp^2+37*bh*h^2*hp^3*bhp+40*bhp*hp^4*bh*h+16*h^5*bh*bhp+21*h^2*bh^2*hp^3+9*hp^5*bh^2+21*h^3*hp^2*bhp^2+40*bh*h^4*bhp*hp+16*hp^5*bhp*bh+23*h*hp^4*bh^2+9*h^5*bhp^2+37*bh*hp^2*bhp*h^3)/((bh+bhp)*bh*bhp*xx^2)));

 

(33)

 

>

 

>