Reliable computation of a multiple integral involved in the neutron star theory Original Research Article

τ(ε,v)=1ω(ε)∫0π/2dθsin⁡(θ)∫0∞dnn2∫0∞dph(n,p,θ,ε,v)h(n,p,θ,ε,v)=ψ(z)ϕ(n−ε−z)+ψ(−z)ϕ(n−ε+z)−ψ(z)ϕ(n+ε−z)−ψ(z)ϕ(n+ε+z)z=p2+(vsin⁡(θ))2,ψ(x)=1exp⁡x+1,ϕ(x)=xexp⁡x−1.The aim is to get a table for image for some values of image in image and then to interpolate for the others. We present a new strategy, using the Gauss–Legendre quadrature formula, which allows to have one code available whatever the values of image and image are. We guarantee the accuracy of the final result including both the truncation error and the round-off error using Discrete Stochastic Arithmetic.