General sampling formula conjecture for Lambda-coalescents
Let Λ\LambdaΛ be a finite measure on [0,1][0,1][0,1] with Λ({1})=0\Lambda(\{1\})=0Λ({1})=0, and let ψ(q)=∫[0,1](e−qx−1+qx)x−2Λ(dx)\psi(q)=\int_{[0,1]}(e^{-qx}-1+qx)x^{-2}\Lambda(dx)ψ(q)=∫[0,1](e−qx−1+qx)x−2Λ(dx). For a sample of size nnn, let XnX_nXn denote eith…