In[]:=
$Version
Out[]=
14.2.0 for Microsoft Windows (64-bit) (December 26, 2024)
(*-FirstMethod-------------------------------------------------------------------------------------------------------------*)
■
We use:
FoxH-
a
2
,12,{},{0,1},
1-a
2
,12,-
a+1
2
,12,{},x//FunctionExpand(*MeijerGthanFoxHfunctionforbettercomputation.*)
Out[]=
MeijerG-
a
2
,{},0,
1
2
,
1
2
(-1-a),
1-a
2
,{},
x
2
,
1
2

π
In[]:=
ClearAll["`*"];Remove["`*"]
In[]:=
K1=2;​​K2=2;​​Ω1=1;​​Ω2=1;​​λ=1;​​p=1;​​M=2;​​ρ=1/2;​​​​q=
πExp[1/2(-K1-K2)]
4
Ω1*Ω2
(K1+1)BesselI0,
K1
2
+K1BesselI1,
K1
2
(K2+1)BesselI0,
K2
2
+K2BesselI1,
K2
2
;​​Vr=
1
16Ω1*Ω2
16(K1+1)(K2+1)-
2
π
Exp[-K1-K2]
2
(K1+1)BesselI0,
K1
2
+K1BesselI1,
K1
2

2
(K2+1)BesselI0,
K2
2
+K2BesselI1,
K2
2

;​​a=
M
2
q
Vr
;​​b=
Vr
q
;
In[]:=
w[γ_]:=N
1
8
4-
2
-1-a
b
p
-1-
a
2
1
2
+
-γ/10
10
(-2+ρ)
-1+ρ
1
2
(-1-a)
(-
γ/5
10
λ(-1+ρ)ρΩ1)
1
Pi
*MeijerG-
a
2
,{},0,
1
2
,
1
2
(-1-a),
1-a
2
,{},
-γ/10
10
p
2
b
λ4-
γ/10
10
(-1+ρ)-2ρρΩ1
2
,
1
2

πGamma[1+a]
,20
In[]:=
w[1]//AbsoluteTiming
Out[]=
{13.4893,0.38912039951752801091+0.×
-21
10
}
In[]:=
data=Table[{γ,w[γ]},{γ,1,50,5}];
In[]:=
ListLinePlot[data]
Out[]=
(*--------------------------------------------------------------------------------------------------------------*)
N
1
8
4-
2
-1-a
b
p
-1-
a
2
1
2
+
-γ/10
10
(-2+ρ)
-1+ρ
1
2
(-1-a)
(-
γ/5
10
λ(-1+ρ)ρΩ1)
*FoxH-
a
2
,12,{},{0,1},
1-a
2
,12,-
a+1
2
,12,{},
-γ/10
10
p
2
b
λ4-
γ/10
10
(-1+ρ)-2ρρΩ1
2

πGamma[1+a]
/.γ->1,1//AbsoluteTiming(*Notsogoodfortimecomputation:*)
Out[]=
$Aborted
(*IAbortednotsoogood!!!*)