Airy T-bar integral

airydelta[p_]:=-ArcTan[p(AiryAi[0-p^2]/AiryAiPrime[0-p^2])]

deltapade[p_]:= ((a1 p+a2 (p^2)+a3 (p^3)+a4 (p^4)+a5 (p^5))/(1+b1 p+b2 (p^2)))

a:=Pi/4

b:=2/3

c:=3^(-1/3)Gamma[1/3]/Gamma[2/3]

d:=1-6Gamma[7/6]^3/Pi^(3/2)

a1:=N[c]

a2:=N[(b-d)a/c]

a3:=N[b]

a4:=N[(b-d)a*b/c^2]

a5:=N[(b-d)b/c]

b1:=N[(b-d)a/c^2]

b2:=N[(b-d)/c]

n := N[1/(8Pi^2)]

N[n c^(-2)]

ruintpade[u_,r_,z_]:= Pi^(-3)r (Sqrt[1-(u^2)]) Cos[2 z r u-2 deltapade[r u]]

u:=0.5

LVpaderiesz1ur[z_,lambda_]:=NIntegrate[(1-(r/lambda))ruintpade[u,r,z],{r,0,lambda},Method->"LevinRule"]

LV1u05=Table[LVpaderiesz1ur[-1,lambda],{lambda,1,100}]

LV1ur1=ListPlot[LV1u05]

u:=0.7

LVpaderiesz1ur[z_,lambda_]:=NIntegrate[(1-(r/lambda))ruintpade[u,r,z],{r,0,lambda},Method->"LevinRule"]

LV1u07=Table[LVpaderiesz1ur[-1,lambda],{lambda,1,100}]

LV1ur2=ListPlot[LV1u07]

u:=0.8

LVpaderiesz1ur[z_,lambda_]:=NIntegrate[(1-(r/lambda))ruintpade[u,r,z],{r,0,lambda},Method->"LevinRule"]

LV1u08=Table[LVpaderiesz1ur[-1,lambda],{lambda,1,100}]

LV1ur3=ListPlot[LV1u08]

u:=0.9

LVpaderiesz1ur[z_,lambda_]:=NIntegrate[(1-(r/lambda))ruintpade[u,r,z],{r,0,lambda},Method->"LevinRule"]

LV1u09=Table[LVpaderiesz1ur[-1,lambda],{lambda,1,100}]

LV1ur4=ListPlot[LV1u09]

u:=0.95

LVpaderiesz1ur[z_,lambda_]:=NIntegrate[(1-(r/lambda))ruintpade[u,r,z],{r,0,lambda},Method->"LevinRule"]

LV1u095=Table[LVpaderiesz1ur[-1,lambda],{lambda,1,100}]

LV1ur5=ListPlot[LV1u095]

GraphicsRow[{LV1ur1,LV1ur2}]

GraphicsRow[{LV1ur3,LV1ur4}]

GraphicsRow[{LV1ur1,LV1ur5}]

u:=0.5

CCpaderiesz1ur[z_,lambda_]:=NIntegrate[(1-(r/lambda))ruintpade[u,r,z],{r,0,lambda},Method->"ClenshawCurtisRule"]

CC1u05=Table[CCpaderiesz1ur[-1,lambda],{lambda,1,100}]

CC1ur1=ListPlot[CC1u05]

u:=0.7

CCpaderiesz1ur[z_,lambda_]:=NIntegrate[(1-(r/lambda))ruintpade[u,r,z],{r,0,lambda},Method->"ClenshawCurtisRule"]

CC1u07=Table[CCpaderiesz1ur[-1,lambda],{lambda,1,100}]

CC1ur2=ListPlot[CC1u07]

u:=0.8

CCpaderiesz1ur[z_,lambda_]:=NIntegrate[(1-(r/lambda))ruintpade[u,r,z],{r,0,lambda},Method->"ClenshawCurtisRule"]

CC1u08=Table[CCpaderiesz1ur[-1,lambda],{lambda,1,100}]

CC1ur3=ListPlot[CC1u08]

u:=0.9

CCpaderiesz1ur[z_,lambda_]:=NIntegrate[(1-(r/lambda))ruintpade[u,r,z],{r,0,lambda},Method->"ClenshawCurtisRule"]

CC1u09=Table[CCpaderiesz1ur[-1,lambda],{lambda,1,100}]

CC1ur4=ListPlot[CC1u09]

u:=0.95

CCpaderiesz1ur[z_,lambda_]:=NIntegrate[(1-(r/lambda))ruintpade[u,r,z],{r,0,lambda},Method->"ClenshawCurtisRule"]

CC1u095=Table[CCpaderiesz1ur[-1,lambda],{lambda,1,100}]

CC1ur5=ListPlot[CC1u095]

GraphicsRow[{CC1ur1,CC1ur2}]

GraphicsRow[{CC1ur3,CC1ur4}]

GraphicsRow[{CC1ur1,CC1ur5}]

Comparision Between Levin and ClenshawCurtis for padereisz0ur

GraphicsRow[{LV1ur1,CC1ur1}]

GraphicsRow[{LV1ur2,CC1ur2}]

GraphicsRow[{LV1ur3,CC1ur3}]

GraphicsRow[{LV1ur4,CC1ur4}]

GraphicsRow[{LV1ur5,CC1ur5}]