I was dealing with a convolution type integral $$ \int^z_0 t^m {}_0F_1(;1;-t) \: {}_2F_3\Big( 1,1;2,m,m+1 ; -a t\Big) \:\mathrm{d}t $$
By applying one of the identities in Exton's book, the solution should be $$\frac{\Gamma(m)}{\Gamma(m+1)} z^m \, \mathrm{F}^{0:3;1}_{1:3;1} \Bigg( \begin{matrix} - &:& m,1,1 &;1& \\ m+1&:& 2,m,m+1&;1& \end{matrix} \Bigg| -az,z \Bigg) $$
any idea how to reduce this form of Kampé de Fériet function into :
(a) a product of hypergeometric functions
(b) any form of Appell or Humbert series.