In[]:=
ClearAll["Global`*"];​​s[x_,n_,η_,k_]:=n*
k
η
*
2k
x
;​​​​(*ThisistheLikliyhoodL(Y|x)whichisproportionaltothenumberofexperimentsdone*)​​likeYX[x_,y_,n_,k_,η_]:=
Power[s[x,n,η,k],y]*Exp[-s[x,n,η,k]]
y!
;​​​​(*onecanseeherethatthesumconvergesto1*)​​likeSum[x_,y_,n_,k_,η_]:=Sum[likeYX[x,y,n,k,η],{y,0,Infinity}]
evidance[x_,y_,n_,k_,η_]:=1/Integrate[likeYX[x,y,n,k,η],{x,0,1}];​​pxn[x_,y_,n_,k_,η_]:=Simplify[likeYX[x,y,n,k,η]*evidance[x,y,n,k,η]];​​numenatorSum[x_,n_,k_,η_]:=Sum[pxn[x,y,n,k,η]*likeYX[x,y,n,k,η],{y,0,Infinity}]​​
Out[]=
∞
∑
y=0
2
-2n
2k
x
k
η

k
1
2
k
n
k
η

2y
n
2k
x
k
η

y!Gamma
1
2k
+y-Gamma
1
2k
+y,n
k
η

if Re[k]>0
(*ClearAll[n,k,η,x];*)​​ListPlot[Table[{x,numenatorSum[x,4,2,0.9]},{x,0.1,1,0.1}]]
Power
:Indeterminate expression
0
0.
encountered.
Power
:Indeterminate expression
0
0.
encountered.
Power
:Indeterminate expression
0
0.
encountered.
General
:Further output of Power::indet will be suppressed during this calculation.
NSum
:The precision of the argument function ​
5.36656
2y
0.
y!Gamma
1
4
+y-Gamma
1
4
+y,3.24
​ is less than WorkingPrecision (​26.​).
​