(* 2020.03.31 *)

(* Sigma = IdentityMatrix[m]/s *)
c1[m_,n_,s_]:=Block[{tt},
tt = 2*(2*Pi)^(n*m/2)*(1/s)^(m*n/2);
Return[1/tt]
]

c2[m_]:=(2*Pi^(m/2)/Gamma[m/2])^2

c3Wrong[m_,s_,sigma_]:=Block[{tt,k},
tt = 1/((m-1)!*2^(m-1));
tt = tt*Exp[-s*sigma^2/2];
tt = tt*(2^(m-2)*Product[Pi^(k/2)/Gamma[k/2],{k,2,m-1}])^2;
Return[tt]
]
c3[m_,s_,sigma_]:=Block[{tt,k},
tt = 1/((m-1)!*2^(m-1)*2^(m-1));
tt = tt*Exp[-s*sigma^2/2];
tt = tt*(2^(m-1)*Pi^((m-1)*m/4)*Product[1/Gamma[k/2],{k,1,m-1}])^2;
Return[tt]
]

c4[m_,s_]:= (s/2)^(-(m^2-1)/2)

c5[m_]:=Product[Gamma[1+i/2]*Gamma[3/2+(i-1)/2]/Gamma[3/2],{i,1,m-1}]*(-1)^(m-1)
(* ec-28-20200331.nb of MathNotebook *)

c12345[m_,n_,s_,sigma_]:=Simplify[c1[m,n,s]*c2[m]*c3[m,s,sigma]*c4[m,s]*c5[m]]

ecSelb[m_,s_,x_]:=NIntegrate[c12345[m,m,s,sigma]*Hypergeometric1F1[-(m-1),1,s*sigma^2],{sigma,x,Infinity}]