Sums of products of q-Euler numbers

By using multivariate fermionic p-adic q-integral on Z(p), the author introduced the q-Euler polynomials of higher order (see [1]). From these q-Euler polynomials of higher order, we derive the formula for the sums of products of the q-Euler polynomials of the form Sigma(r=i1 +...+il)(i1, ... ,il >= 0) Sigma(r-il)(k1=0)...Sigma(r-i1-i2-...-il-1)(kl-1=0) ((r)(il,...,il))((r-il)(k1))...((r-i1-i2-...il-1)(kl-1))E-k1+i1,E-q(alpha(1))...E(kl-1+)i(l-1,q)(alpha(l-1))Ei(l,q)(alpha(l))(q-1)(n)(k1+...+kl-1), where E-m,E-q(alpha) are the m-th q-Euler polynomials and ((alpha 1,...,alpha n) (n)) = n!/alpha(1)!...alpha(n)!.