(*theplotofTvsxisrequired*)​​(*THEACTUALEQUATION,sol=
∞
∫
0
x
-k-1
1+
x
k-
3
2
T
x==
∞
∫
0
x
-k-1
1+
x
k-
3
2
T

-
x
a
c
-
-x
b
c
-
-Cx
B
+Ax,A=0.3136,B=0.0692,C=0.6207,a=1.29,b=0.1101,c=3.014,k=2.5*)​​sol=
∞
∫
0
x
-2.5-1
1+
x
2.5-
3
2
T
x==
∞
∫
0
x
-2.5-1
1+
x
2.5-
3
2
T
3.014
-
x
1.29

-3.014
-x
0.1101

-0.0692
-0.6207x

+0.3136x​​ContourPlot[sol,{x,2,10},{T,0,1}](*anattempttoplotthesolutionofaboveequation*)
ConditionalExpression0.266667
2
T

1
8.

1
T

5.
1
T
0.0458159HypergeometricPFQ[{2},{0.75,0.25},0.0963171
2
T
]-2.4922HypergeometricPFQ[{2},{0.75,0.25},0.150231
2
T
]+29.2001HypergeometricPFQ[{2},{0.75,0.25},20.6236
2
T
]+
6.
1
T
0.0836267-0.0184533HypergeometricPFQ1,
3
2
,0.25,-0.25,
1
2
,0.0963171
2
T
+0.803733HypergeometricPFQ1,
3
2
,0.25,-0.25,
1
2
,0.150231
2
T
-0.803733HypergeometricPFQ1,
3
2
,0.25,-0.25,
1
2
,20.6236
2
T
+
4.5
1
T
-0.0399864HypergeometricPFQ[{1.75,2.25},{1.75,0.5,1.25},0.0963171
2
T
]+2.43076HypergeometricPFQ[{1.75,2.25},{1.75,0.5,1.25},0.150231
2
T
]-97.4868HypergeometricPFQ[{1.75,2.25},{1.75,0.5,1.25},20.6236
2
T
]-0.0399864HypergeometricPFQ[{2.25,1.75},{1.25,0.5,1.75},0.0963171
2
T
]+2.43076HypergeometricPFQ[{2.25,1.75},{1.25,0.5,1.75},0.150231
2
T
]-97.4868HypergeometricPFQ[{2.25,1.75},{1.25,0.5,1.75},20.6236
2
T
]+
3.5
1
T
-0.0347474HypergeometricPFQ[{2.25,2.75},{2.25,1.5,1.75},0.0963171
2
T
]+2.63804HypergeometricPFQ[{2.25,2.75},{2.25,1.5,1.75},0.150231
2
T
]-1239.61HypergeometricPFQ[{2.25,2.75},{2.25,1.5,1.75},20.6236
2
T
]-0.0347474HypergeometricPFQ[{2.75,2.25},{1.75,1.5,2.25},0.0963171
2
T
]+2.63804HypergeometricPFQ[{2.75,2.25},{1.75,1.5,2.25},0.150231
2
T
]-1239.61HypergeometricPFQ[{2.75,2.25},{1.75,1.5,2.25},20.6236
2
T
],Re[T]≥0&&2Arg
1
T
≤π||Im[T]>0
​