ver1:23Aug 2018
ver2:19 Oct 2018,corrected typo for Vϵ3, (Vϵ3 in ver1 should be devided by f=1-2M/r)

effective potentials for (Subscript[ϵ, 1]) correction

((d^2)/(Subscript[dr, *]^2))Ψmϵ1  +((ω^2) - (Sqrt[ft fr])(VmGR + ϵ1 Vmϵ1 ))Ψmϵ1  = 0
((d^2)/(Subscript[dr, *]^2))Ψpϵ1  +((ω^2) - (Sqrt[ft fr])(VpGR + ϵ1 Vpϵ1 ))Ψpϵ1  = 0
where  (d/(SubStar[dr]))=(Sqrt[ft fr])(d/dr)
 All equations make sence up to O(ϵ1)

(* background black hole solution *) 
g={{ft,0,0,0},{0,(1/fr),0,0},{0,0,(r^2),0},{0,0,0,(r^2) ((Sin[θ])^2)}};
ft=1-((2 M)/r)+((128 (M^9) (11 M-8 r) ϵ1 )/(r^10));
fr=1-((2 M)/r)+((128 (M^9) (67 M-36 r) ϵ1 )/(r^10));
(* ft and fr take O(((ϵ1)^2)) at r = rH *)
rH= 2 M + ϵ1((5 M)/(4 )); (* M=(rH/2)-ϵ1 rH (5/16); *)

(* even and odd parity perturbation in the Regge-Wheeler gauge *)
(* YL0[θ] is the spherical harmonics (Subscript[Y, ℓm]) with ℓ=L and m=0 *)
hodd=(E^(-I t ω))Sin[θ] YL0'[θ]{{0,0,0, h0[r] },{0,0,0, h1[r] },{0,0,0,0},{ h0[r],h1[r],0,0}};
heven=(E^(-I t ω))YL0[θ]{{ ft  H0[r] , H1[r] ,0,0},{ H1[r],(( H2[r])/fr),0,0},{0,0, (r^2) K[r] ,0},{0,0,0,(r^2) K[r] ((Sin[θ])^2) }};

(* master variables *)
Ψmϵ1=(Sqrt[ft fr])((I  h1[r])/( ω r))(1+((1152 (M^8) (13 M-7 r)ϵ1)/(r^9)));
Ψpϵ1=((I  H1[r])/ω)(((Sqrt[ft fr])((r^9) (6 M+(-2+L (L+1)) r)-128 (M^8) ϵ1(-162 (M^2)+(98+23 L (L+1)) M r+3 (L-1) L (L+1) (L+2) (r^2)) ))/((r^8) (((6 M+(-2+L (L+1)) r))^2) )) -((K[r]((r^9) (6 M+(-2+L (L+1)) r)-384 (M^8) ϵ1(-82 (M^2)+3 (14+L+(L^2)) M r+(-1+L) L (1+L) (2+L) (r^2)) ))/((r^7) (((6 M+(-2+L (L+1)) r))^2))) ;

(* effective potentials for odd mode *)
VmGR=((-6 M+L (1+L) r)/(r^3));
Vmϵ1=-((256 (M^8)  (15561 (M^2)+(-13509+146 L (1+L)) M r+9 (r^2) (324-8 L (1+L)+7 (r^2) (ω^2))))/(r^12));

(* effective potentials for even mode *)
VpGR=((72 (M^3)+36 (-2+L+(L^2)) (M^2) r+6 (((-2+L+(L^2)))^2) M (r^2)+L (1+L) (((-2+L+(L^2)))^2) (r^3))/((r^3) (((6 M+(-2+L+(L^2)) r))^2)));
Vpϵ1=((128 (M^8))/((r^12) (((6 M+(-2+L+(L^2)) r))^3)))(230688 (M^5)+144 (-4643+1984 L (1+L)) (M^4) r+36 (-1+L) (2+L) (-10132+2249 L (1+L)) (M^3) (r^2)+18 (-1+L) (2+L) (10696+L (1+L) (-4982+321 L (1+L))) (M^2) (r^3)-10 (((-2+L+(L^2)))^2) (-2502+L (1+L) (469+13 L (1+L))) M (r^4)+9 (((-2+L+(L^2)))^3) (144+L (1+L) (14+L+(L^2))) (r^5)-126 (r^4) (((6 M+(-2+L+(L^2)) r))^3) (ω^2));

(* relation among perturbed metric and master variables *)
(*
h0[r]=(1-((2 M)/r)) (Ψmϵ1[r]+r (Ψmϵ1)'[r])-((128 (M^8) ϵ1 ((2661 (M^2)-2462 M r+567 (r^2)) Ψmϵ1[r]+r (231 (M^2)-239 M r+63 (r^2)) (Ψmϵ1)'[r]))/(r^10));
h1[r]=((I (r^2) ω Ψmϵ1[r])/(2 M-r))-((128 I (M^8) (195 (M^2)-221 M r+63 (r^2)) ϵ1 ω Ψmϵ1[r])/((r^7) (((-2 M+r))^2)));
*)

(* relation among perturbed metric and master variables *)
(*
H0[r]=(1/((r^2) (((6 M+(-2+L+(L^2)) r))^2)))(1/(2 M-r)(-144 (M^4)-72 (-3+L+(L^2)) (M^3) r+(((-2+L+(L^2)))^2) (r^4) (L+(L^2)-2 (r^2) (ω^2))-12 (M^2) (r^2) (10+L (1+L) (-7+L+(L^2))+6 (r^2) (ω^2))-2 (-2+L+(L^2)) M (r^3) (6-5 L-4 (L^2)+2 (L^3)+(L^4)+12 (r^2) (ω^2))) Ψpϵ1[r]+2 r (6 M+(-2+L+(L^2)) r) (6 (M^2)+3 (-2+L+(L^2)) M r-(-2+L+(L^2)) (r^2)) (Ψpϵ1)'[r])+(128 (M^8) ϵ1 (M (11 M-8 r) (6 M+(-2+L+(L^2)) r) (1/(2 M-r)(-144 (M^4)-72 (-3+L+(L^2)) (M^3) r+(((-2+L+(L^2)))^2) (r^4) (L+(L^2)-2 (r^2) (ω^2))-12 (M^2) (r^2) (10+L (1+L) (-7+L+(L^2))+6 (r^2) (ω^2))-2 (-2+L+(L^2)) M (r^3) (6-5 L-4 (L^2)+2 (L^3)+(L^4)+12 (r^2) (ω^2))) Ψpϵ1[r]+2 r (6 M+(-2+L+(L^2)) r) (6 (M^2)+3 (-2+L+(L^2)) M r-(-2+L+(L^2)) (r^2)) (Ψpϵ1)'[r])+1/(2 M-r)(1-((2 M)/r)) r (-(1296 (M^6)+144 (-649+434 L (1+L)) (M^5) r-6 (((-2+L+(L^2)))^3) (48+L (1+L) (1+L+(L^2))) (r^6)+72 (-2+L+(L^2)) (M^3) (r^3) (1343+L (1+L) (-767+68 L (1+L))+27 (r^2) (ω^2))+144 (M^4) (r^2) (1454+L (1+L) (-1269+244 L (1+L))+27 (r^2) (ω^2))+(((-2+L+(L^2)))^2) (M^2) (r^4) (22992+L (1+L) (-5636+115 L (1+L))+324 (r^2) (ω^2))+(((-2+L+(L^2)))^2) M (r^5) (-36 (157+(r^2) (ω^2))+L (1+L) (2156+L (1+L) (-67+12 L (1+L))+18 (r^2) (ω^2)))) Ψpϵ1[r]-2 r (6 M+(-2+L+(L^2)) r) (5724 (M^5)+12 (-916+227 L (1+L)) (M^4) r+3 (2812+L (1+L) (-1472+141 L (1+L))) (M^3) (r^2)-2 (-1+L) (2+L) (-833+250 L (1+L)) (M^2) (r^3)+179 (((-2+L+(L^2)))^2) M (r^4)-18 (((-2+L+(L^2)))^2) (r^5)) (Ψpϵ1)'[r])))/((1-((2 M)/r)) (r^12) (((6 M+(-2+L+(L^2)) r))^3));
H1[r]=2 I ω ((((6 (M^2)+3 (-2+L+(L^2)) M r-(-2+L+(L^2)) (r^2)) Ψpϵ1[r])/((2 M-r) (6 M+(-2+L+(L^2)) r)))+r (Ψpϵ1)'[r])-(1/(r^9))256 I (M^8) ϵ1 ω (((14580 (M^5)+372 (-100+29 L (1+L)) (M^4) r+3 (12872+L (1+L) (-6748+507 L (1+L))) (M^3) (r^2)-2 (-1+L) (2+L) (-5081+1063 L (1+L)) (M^2) (r^3)+108 (-1+L) (2+L) (-25+9 L (1+L)) M (r^4)-144 (((-2+L+(L^2)))^2) (r^5)) Ψpϵ1[r])/((((-2 M+r))^2) (((6 M+(-2+L+(L^2)) r))^2))-9 M r (Ψpϵ1)'[r]);
H2[r]=(1/((r^2) (((6 M+(-2+L+(L^2)) r))^2)))(1/(-2 M+r)(144 (M^4)+72 (-3+L+(L^2)) (M^3) r-(((-2+L+(L^2)))^2) (r^4) (L+(L^2)-2 (r^2) (ω^2))+12 (M^2) (r^2) (10+L (1+L) (-7+L+(L^2))+6 (r^2) (ω^2))+2 (-2+L+(L^2)) M (r^3) (6+L (1+L) (-5+L+(L^2))+12 (r^2) (ω^2))) Ψpϵ1[r]+2 r (6 M+(-2+L+(L^2)) r) (6 (M^2)+3 (-2+L+(L^2)) M r-(-2+L+(L^2)) (r^2)) (Ψpϵ1)'[r])+(1/((r^11) (((6 M+(-2+L+(L^2)) r))^3)))128 (M^8) (1-((2 M)/r)) ϵ1 (-1/(((-2 M+r))^2)M (67 M-36 r) r (6 M+(-2+L+(L^2)) r) (1/(-2 M+r)(144 (M^4)+72 (-3+L+(L^2)) (M^3) r-(((-2+L+(L^2)))^2) (r^4) (L+(L^2)-2 (r^2) (ω^2))+12 (M^2) (r^2) (10+L (1+L) (-7+L+(L^2))+6 (r^2) (ω^2))+2 (-2+L+(L^2)) M (r^3) (6+L (1+L) (-5+L+(L^2))+12 (r^2) (ω^2))) Ψpϵ1[r]+2 r (6 M+(-2+L+(L^2)) r) (6 (M^2)+3 (-2+L+(L^2)) M r-(-2+L+(L^2)) (r^2)) (Ψpϵ1)'[r])+1/(1-((2 M)/r))(1/(((-2 M+r))^2)(489888 (M^7)+144 (-8011+1124 L (1+L)) (M^6) r-12 (((-2+L+(L^2)))^3) (r^7) (24+L (1+L) (10+L+(L^2))-21 (r^2) (ω^2))+(M^2) (r^5) (-(((-2+L+(L^2)))^2) (-16248+L (1+L) (320+L (1+L) (569+48 L (1+L))))+12 (-1+L) (2+L) (5246+L (1+L) (-1625+68 L (1+L))) (r^2) (ω^2))+(((-2+L+(L^2)))^2) M (r^6) (-5292+6340 (r^2) (ω^2)+L (1+L) (84+3 L (1+L) (143+16 L (1+L))-902 (r^2) (ω^2)))+144 (M^4) (r^3) (-2746-2577 (r^2) (ω^2)-L (1+L) (-754+L (1+L) (-191+15 L (1+L))-612 (r^2) (ω^2)))-144 (M^5) (r^2) (2 L (1+L) (940+37 L (1+L))-3 (2425+408 (r^2) (ω^2)))+2 (M^3) (r^4) (552 (-13+279 (r^2) (ω^2))+L (1+L) (29828-78084 (r^2) (ω^2)+L (1+L) (L (1+L) (504+95 L (1+L))+36 (-403+204 (r^2) (ω^2)))))) Ψpϵ1[r]-1/(2 M-r)2 r (6 M+(-2+L+(L^2)) r) (26244 (M^5)+12 (-4720+1223 L (1+L)) (M^4) r+3 (16868+L (1+L) (-8476+615 L (1+L))) (M^3) (r^2)-2 (-1+L) (2+L) (-5891+1225 L (1+L)) (M^2) (r^3)+27 (-1+L) (2+L) (-106+39 L (1+L)) M (r^4)-144 (((-2+L+(L^2)))^2) (r^5)) (Ψpϵ1)'[r]));
K[r]=((-(((24 (M^2)+6 (-2+L+(L^2)) M r+(-1+L) L (1+L) (2+L) (r^2)) Ψpϵ1[r])/(6 M+(-2+L+(L^2)) r))+2 (2 M-r) r (Ψpϵ1)'[r])/(r^2))+(1/(r^11))128 (M^8) ϵ1 (-1/(((6 M+(-2+L+(L^2)) r))^2)3 (2712 (M^4)+8 (-949+407 L (1+L)) (M^3) r+4 (-1+L) (2+L) (-889+141 L (1+L)) (M^2) (r^2)+3 (-1+L) (2+L) (460+L (1+L) (-156+5 L (1+L))) M (r^3)+(((-2+L+(L^2)))^2) (96+(-1+L) L (1+L) (2+L)) (r^4)) Ψpϵ1[r]+2 M r (-49 M+27 r) (Ψpϵ1)'[r]);
*)

effective potentials for (Subscript[ϵ, 2]) correction

((d^2)/(Subscript[dr, *]^2))Ψmϵ2  +((ω^2) - f(VmGR + ϵ2 Vmϵ2 ))Ψmϵ2  = 0
((d^2)/(Subscript[dr, *]^2))Ψpϵ2  +((ω^2) - f(VpGR + ϵ2 Vpϵ2 ))Ψpϵ2 = 0
where  (d/(SubStar[dr]))=f(d/dr)

(* back ground black hole solution *)
g={{f,0,0,0},{0,(1/f),0,0},{0,0,(r^2),0},{0,0,0,(r^2) ((Sin[θ])^2)}};
f=1-((2 M)/r);

(* even and odd parity perturbation in the Regge-Wheeler gauge *)
(* YL0[θ] is the spherical harmonics (Subscript[Y, ℓm]) with ℓ=L and m=0 *)
hodd=(E^(-I t ω))Sin[θ] YL0'[θ]{{0,0,0, h0[r] },{0,0,0, h1[r] },{0,0,0,0},{ h0[r],h1[r],0,0}};
heven=(E^(-I t ω))YL0[θ]{{ f  H0[r] , H1[r] ,0,0},{ H1[r],(( H2[r])/f),0,0},{0,0, (r^2) K[r] ,0},{0,0,0,(r^2) K[r] ((Sin[θ])^2) }};

(* master variables *)
Ψmϵ2=f((I h1[r])/( ω r));
Ψpϵ2=(1/(6 M+(-2+L+(L^2)) r))(r f((I H1[r])/ω)-(r^2) K[r]);

(* effective potentials for odd mode *)
VmGR=((-6 M+L (1+L) r)/(r^3));
Vmϵ2=((4608 (-1+L) L (1+L) (2+L) (M^8))/(r^10));

(* effective potentials for even mode *)
(* even parity perturbation is same as GR *)
VpGR=((72 (M^3)+36 (-2+L+(L^2)) (M^2) r+6 (((-2+L+(L^2)))^2) M (r^2)+L (1+L) (((-2+L+(L^2)))^2) (r^3))/((r^3) (((6 M+(-2+L+(L^2)) r))^2)));
Vpϵ2=0;

(* relation among perturbed metric and master variables *)
(*
h0[r]=(1-((2 M)/r)) (Ψmϵ2[r]+r (Ψmϵ2)'[r]);
h1[r]=((I (r^2) ω Ψmϵ2[r])/(2 M-r));
*)

(* relation among perturbed metric and master variables *)
(*
H0[r]=(1/((r^2) (((6 M+(-2+L+(L^2)) r))^2)))(1/(2 M-r)(-144 (M^4)-72 (-3+L+(L^2)) (M^3) r+(((-2+L+(L^2)))^2) (r^4) (L+(L^2)-2 (r^2) (ω^2))-12 (M^2) (r^2) (10+L (1+L) (-7+L+(L^2))+6 (r^2) (ω^2))-2 (-2+L+(L^2)) M (r^3) (6-5 L-4 (L^2)+2 (L^3)+(L^4)+12 (r^2) (ω^2))) Ψpϵ2[r]+2 r (6 M+(-2+L+(L^2)) r) (6 (M^2)+3 (-2+L+(L^2)) M r-(-2+L+(L^2)) (r^2)) (Ψpϵ2)'[r]);
H1[r]=2 I ω ((((6 (M^2)+3 (-2+L+(L^2)) M r-(-2+L+(L^2)) (r^2)) Ψpϵ2[r])/((2 M-r) (6 M+(-2+L+(L^2)) r)))+r (Ψpϵ2)'[r]);
H2[r]=(1/((r^2) (((6 M+(-2+L+(L^2)) r))^2)))(1/(-2 M+r)(144 (M^4)+72 (-3+L+(L^2)) (M^3) r-(((-2+L+(L^2)))^2) (r^4) (L+(L^2)-2 (r^2) (ω^2))+12 (M^2) (r^2) (10+L (1+L) (-7+L+(L^2))+6 (r^2) (ω^2))+2 (-2+L+(L^2)) M (r^3) (6+L (1+L) (-5+L+(L^2))+12 (r^2) (ω^2))) Ψpϵ2[r]+2 r (6 M+(-2+L+(L^2)) r) (6 (M^2)+3 (-2+L+(L^2)) M r-(-2+L+(L^2)) (r^2)) (Ψpϵ2)'[r]);
K[r]=-(((24 (M^2)+6 (-2+L+(L^2)) M r+(-1+L) L (1+L) (2+L) (r^2)) Ψpϵ2[r])/((r^2) (6 M+(-2+L+(L^2)) r)))+(-2+((4 M)/r)) (Ψpϵ2)'[r];
*)

effective potentials for (Subscript[ϵ, 3]) correction

((d^2)/(Subscript[dr, *]^2))(({{Ψmϵ3tilde}, {Ψpϵ3tilde}}))+(({{(ω^2)-f VmGR, -ϵ3 f Vϵ3}, {-ϵ3 f Vϵ3, (ω^2)-f VpGR}})) (({{Ψmϵ3tilde}, {Ψpϵ3tilde}}))=0 
where  (d/(SubStar[dr]))=f(d/dr)
there is coupling between even and odd modes

(* back ground black hole solution *)
g={{f,0,0,0},{0,(1/f),0,0},{0,0,(r^2),0},{0,0,0,(r^2) ((Sin[θ])^2)}};
f=1-((2 M)/r);

(* even and odd parity perturbation in the Regge-Wheeler gauge *)
(* YL0[θ] is the spherical harmonics (Subscript[Y, ℓm]) with ℓ=L and m=0 *)
hodd=(E^(-I t ω))Sin[θ] YL0'[θ]{{0,0,0, h0[r] },{0,0,0, h1[r] },{0,0,0,0},{ h0[r],h1[r],0,0}};
heven=(E^(-I t ω))YL0[θ]{{f  H0[r] , H1[r] ,0,0},{ H1[r],(( H2[r])/f),0,0},{0,0, (r^2) K[r] ,0},{0,0,0,(r^2) K[r] ((Sin[θ])^2) }};

(* master variables *)
Ψmϵ3tilde=Ψmϵ3[r]+((64 (M^8) (888 (M^2)+2 (-355+56 L (1+L)) M r-63 (-2+L+(L^2)) (r^2)) ϵ3 Ψpϵ3[r])/((r^9) (6 M+(-2+L+(L^2)) r)))-((1152 (M^8) (2 M-r) ϵ3 (Ψpϵ3)'[r])/(r^8));
Ψpϵ3tilde=Ψpϵ3[r]+((64 (M^8) (1056 (M^2)+2 (-383+70 L (1+L)) M r+3 (-1+L) (2+L) (-21+2 L (1+L)) (r^2)) ϵ3 Ψmϵ3[r])/((r^9) (6 M+(-2+L+(L^2)) r)))-((1152 (M^8) (-2 M+r) ϵ3 (Ψmϵ3)'[r])/(r^8));
(* with *)
Ψmϵ3[r]=f((I h1[r])/( ω r));
Ψpϵ3[r]=(1/(6 M+(-2+L+(L^2)) r))(r f((I H1[r])/ω)-(r^2) K[r]);

(* effective potentials *)
VmGR=((-6 M+L (1+L) r)/(r^3));
VpGR=((72 (M^3)+36 (-2+L+(L^2)) (M^2) r+6 (((-2+L+(L^2)))^2) M (r^2)+L (1+L) (((-2+L+(L^2)))^2) (r^3))/((r^3) (((6 M+(-2+L+(L^2)) r))^2)));
Vϵ3=((-1)/((r^12) (((6 M+(-2+L+(L^2)) r))^2)))384 (M^8) (203280 (M^4)+2400 (-132+31 L (1+L)) (M^3) r+4 (46321+L (1+L) (-22394+1743 L (1+L))) (M^2) (r^2)+36 (-1+L) (2+L) (671+L (1+L) (-162+L+(L^2))) M (r^3)+3 (((-2+L+(L^2)))^2) (396+(-1+L) L (1+L) (2+L)) (r^4));

(* relation among perturbed metric and master variables *)
(*
h0[r]=(1-((2 M)/r)) (Ψmϵ3[r]+r (Ψmϵ3)'[r])+((16128 (M^8) (1-((2 M)/r)) ϵ3 ((((6 (M^2)+3 (-2+L+(L^2)) M r-(-2+L+(L^2)) (r^2)) Ψpϵ3[r])/(6 M+(-2+L+(L^2)) r))+(2 M-r) r (Ψpϵ3)'[r]))/(r^9));
h1[r]=((I (r^2) ω Ψmϵ3[r])/(2 M-r));
*)

(* relation among perturbed metric and master variables *)
(*
H0[r]=(1/((r^10) (((6 M+(-2+L+(L^2)) r))^2)))384 (-2+L+(L^2)) (M^8) ϵ3 (1/(2 M-r)(3312 (M^4)+24 (-249+46 L (1+L)) (M^3) r-12 (-356+L (1+L) (114+7 L (1+L))) (M^2) (r^2)+2 M (r^3) (-720+L (1+L) (264+L (1+L) (37+L+(L^2))-6 (r^2) (ω^2)))-(-1+L) (2+L) (r^4) (96+L (1+L) (18+L+(L^2)+2 (r^2) (ω^2)))) Ψmϵ3[r]+2 r (216 (M^3)+42 (-6+L+(L^2)) (M^2) r+3 (-8+L+(L^2)) (-4+L+(L^2)) M (r^2)-(-2+L) (-1+L) (2+L) (3+L) (r^3)) (Ψmϵ3)'[r])+(1/((r^2) (((6 M+(-2+L+(L^2)) r))^2)))(1/(2 M-r)(-144 (M^4)-72 (-3+L+(L^2)) (M^3) r+(((-2+L+(L^2)))^2) (r^4) (L+(L^2)-2 (r^2) (ω^2))-12 (M^2) (r^2) (10+L (1+L) (-7+L+(L^2))+6 (r^2) (ω^2))-2 (-2+L+(L^2)) M (r^3) (6-5 L-4 (L^2)+2 (L^3)+(L^4)+12 (r^2) (ω^2))) Ψpϵ3[r]+2 r (6 M+(-2+L+(L^2)) r) (6 (M^2)+3 (-2+L+(L^2)) M r-(-2+L+(L^2)) (r^2)) (Ψpϵ3)'[r]);
H1[r]=-((768 I (M^8) ϵ3 ω ((((-2+L+(L^2)) (-204 (M^2)+(198+13 L (1+L)) M r-(48+7 L (1+L)) (r^2)) Ψmϵ3[r])/(2 M-r))-(-1+L) L (1+L) (2+L) (r^2) (Ψmϵ3)'[r]))/((r^8) (6 M+(-2+L+(L^2)) r)))+2 I ω ((((6 (M^2)+3 (-2+L+(L^2)) M r-(-2+L+(L^2)) (r^2)) Ψpϵ3[r])/((2 M-r) (6 M+(-2+L+(L^2)) r)))+r (Ψpϵ3)'[r]);
H2[r]=(1/((r^11) (((6 M+(-2+L+(L^2)) r))^2)))384 (M^8) ϵ3 (1/(2 M-r)(36288 (M^5)+144 (-466+65 L (1+L)) (M^4) r+2 (-2+L+(L^2)) M (r^4) (-972+672 (r^2) (ω^2)+L (1+L) (2+L (1+L) (101+3 L (1+L))-90 (r^2) (ω^2)))+24 (M^3) (r^2) (5 L (1+L) (-121+2 L (1+L))+36 (57-7 (r^2) (ω^2)))+(((-2+L+(L^2)))^2) (r^5) (-96+84 (r^2) (ω^2)-L (1+L) (56+3 L (1+L)+2 (r^2) (ω^2)))+12 (M^2) (r^3) (-1552+588 (r^2) (ω^2)-L (1+L) (-682+L (1+L) (-18+17 L (1+L))+168 (r^2) (ω^2)))) Ψmϵ3[r]+2 r (9072 (M^4)+1080 (-13+3 L (1+L)) (M^3) r+42 (192+L (1+L) (-92+7 L (1+L))) (M^2) (r^2)+3 (-1+L) (2+L) (340+L (1+L) (-82+L+(L^2))) M (r^3)-(-48+L+(L^2)) (((-2+L+(L^2)))^2) (r^4)) (Ψmϵ3)'[r])+(1/((r^2) (((6 M+(-2+L+(L^2)) r))^2)))(1/(-2 M+r)(144 (M^4)+72 (-3+L+(L^2)) (M^3) r-(((-2+L+(L^2)))^2) (r^4) (L+(L^2)-2 (r^2) (ω^2))+12 (M^2) (r^2) (10+L (1+L) (-7+L+(L^2))+6 (r^2) (ω^2))+2 (-2+L+(L^2)) M (r^3) (6+L (1+L) (-5+L+(L^2))+12 (r^2) (ω^2))) Ψpϵ3[r]+2 r (6 M+(-2+L+(L^2)) r) (6 (M^2)+3 (-2+L+(L^2)) M r-(-2+L+(L^2)) (r^2)) (Ψpϵ3)'[r]);
K[r]=-(((24 (M^2)+6 (-2+L+(L^2)) M r+(-1+L) L (1+L) (2+L) (r^2)) Ψpϵ3[r])/((r^2) (6 M+(-2+L+(L^2)) r)))+(1/((r^10) (6 M+(-2+L+(L^2)) r)))768 (M^8) ϵ3 (-(-2+L+(L^2)) (-204 (M^2)+(198+13 L (1+L)) M r-(48+7 L (1+L)) (r^2)) Ψmϵ3[r]+(-1+L) L (1+L) (2+L) (2 M-r) (r^2) (Ψmϵ3)'[r])+(-2+((4 M)/r)) (Ψpϵ3)'[r];
*)