∞
∫
0
x
-k-1
1+
x
k-
3
2
T
x(*incidentelectroncurrent*)
ConditionalExpression
2
-
3
2
+k
2
T
(-1+k)k
,2Arg
1
-
3
2
+kT
≤π&&Re[k]>1&&Re
3
2
-kT≤0||
3
2
-kT∉Reals
∞
∫
0
x
-k-1
1+
x
k-
3
2
T

-
x
a
c
-
-x
b
c
-
-Cx
B
+Ax(*outgoingelectroncurrent*)
ConditionalExpression
1
Gamma[1+k]
1
4
A
2
(3-2k)
2
T
Gamma[-1+k]-
1
4
-Cx
B
2
(3-2k)
2
T
Gamma[-1+k]+
1
Log[c]
-k
2
2
-
3
2
+k
1-k
1
(-3+2k)T
2
T
2akπCsc[kπ]Hypergeometric1F11+k,k,
(-3+2k)TLog[c]
2a

k
Log[c]
a
-(-1+k)Gamma[-1+k]
k
2
-1+k
1
(-3+2k)T
Log[c]+
(-3+2k)T
2a
c
Gamma[1-k]
k
Log[c]
a
(2ak+(-3+2k)TLog[c])-
(-3+2k)T
2a
c
Gamma1-k,
(-3+2k)TLog[c]
2a

k
Log[c]
a
(2ak+(-3+2k)TLog[c])-
1
Log[c]
-k
2
2
-
3
2
+k
1-k
1
(-3+2k)T
2
T
2bkπCsc[kπ]Hypergeometric1F11+k,k,
(-3+2k)TLog[c]
2b

k
Log[c]
b
-(-1+k)Gamma[-1+k]
k
2
-1+k
1
(-3+2k)T
Log[c]+
(-3+2k)T
2b
c
Gamma[1-k]
k
Log[c]
b
(2bk+(-3+2k)TLog[c])-
(-3+2k)T
2b
c
Gamma1-k,
(-3+2k)TLog[c]
2b

k
Log[c]
b
(2bk+(-3+2k)TLog[c]),2Arg
1
-
3
2
+kT
≤π&&Re[k]>1&&Re
3
2
-kT≤0||
3
2
-kT∉Reals&&Re
Log[c]
a
>0&&Re
Log[c]
b
>0
​​​​​​(*Plotoftheequationoftheabovetwointegralsisrequired*)​​k=5.5(*kcantakeanyvalue,neededforplotting*)​​(*theplotofTvsxisrequired*)​​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(*Togetthesolutionofbothasanequation*)​​(*A=0.3136,B=0.0692,C=0.6207,a=1.29,b=0.1101,c=3.014*)​​Plot[[Re[sol]],{x,2,10},PlotRangeAll(*anattempttoplotthesolutionofaboveequation*)
5.5
ConditionalExpression0.646465
2
T
0.00347361
2
T
186.108A-186.108
-Cx
B
+16.11.6317Hypergeometric1F12,-3.5,
4.TLog[c]
a
-
8846.72
4.T
a
c
4.5
Log[c]
a
(a+0.727273TLog[c])
a
4.5

1
T

-16.11.6317Hypergeometric1F12,-3.5,
4.TLog[c]
b
-
8846.72
4.T
b
c
4.5
Log[c]
b
(b+0.727273TLog[c])
b
4.5

1
T

,Re
Log[c]
a
>0&&Re
Log[c]
b
>0&&2Arg
1
T
≤π&&(Re[T]≥0||(Im[T]>0&&T∉Reals))&&Re[T]≥0&&2Arg
1
T
≤π||Im[T]>0