Im trying to integrate the following:
\begin{equation} \int_{-1}^{1}\int_{-1}^{1}\int_{-1}^{x} J_{3/4}(x^2 z)J_{1/4}(y^2z) dy dz dx \end{equation}
So what I did was this
i1[x_?NumericQ, z_?NumericQ] :=
i1[x, z] = NIntegrate[BesselJ[1/4, y^2 z], {y, -1, x}]
i2[x_?NumericQ] :=
i2[x] = NIntegrate[BesselJ[3/4, x^2 z] i1[x, z], {z, -1, 1}]
NIntegrate[i2[x], {x, -1, 1}]
Is this correct? And if so, is there any other way to make this faster?
Thanks in advance.