The gfun[`diffeq+diffeq`](eq1, eq2, y(z)) command determines the differential equation satisfied by the sum of two holonomic functions, eq1 and eq2.

If f and g are holonomic function solutions of eq1 and eq2, respectively, the gfun[`diffeq+diffeq`] function returns a linear differential equation verified by .

The differential order of the returned equation is at most the sum of eq1 and eq2's differential orders for the gfun[`diffeq+diffeq`] function.

The gfun[`diffeq*diffeq`](eq1, eq2, y(z)) command determines the differential equation satisfied by the Cauchy product of two holonomic functions, eq1 and eq2.

If f and g are holonomic function solutions of eq1 and eq2), respectively, the gfun[`diffeq*diffeq`] function returns a linear differential equation verified by .

The differential order of the returned equation is at most the product of eq1 and eq2's differential orders for the gfun[`diffeq*diffeq`] function.

The gfun[hadamardproduct](eq1, eq2, y(z)) command determines the differential equation satisfied by the Hadamard product of two holonomic functions, eq1 and eq2.

If f and g are holonomic function solutions of eq1 and eq2, respectively, the gfun[hadamardproduct] function returns a linear differential equation verified by the Hadamard product of f and g.  The function whose coefficient of  in the Taylor expansion around 0 is the product of the corresponding coefficients of f and g.