Derive a holonomic system for the inner triple integral  of the expection of an Euler characteristic number

<< RISC`HolonomicFunctions`; (* load Christoph's package *)

HolonomicFunctions Package version 1.7.3 (21-Mar-2017)
written by Christoph Koutschan
Copyright Research Institute for Symbolic Computation (RISC),
Johannes Kepler University, Linz, Austria

ann2 = <<ec1_ann2.m; (* input a D-finite system of the inner double integral *)

supp3 = Table[ Der[d]^i,{i, 0, 10}] (* a support set for annihilator of the inner triple integral *)

Timing[ann3=FindCreativeTelescoping[ann2,Der[b], Support -> supp3][[1,1]];] (* compute a D-finite ann3 of the inner triple integral with support in supp3 *)

ann3 >> ec1_ann3.m; (* output ann3 *)