It doesn't help to ASSUME(0<z,z<1), because call to
integrate(2/(1-z^2),z) returns log(z+1)-log(z-1), which is wrong when
z<1! In this case, INTEGRATIONCONSTANT is necessary, it equals to
log(-1), so that log(z-1)-log(-1) turns into log(1-z), which is correct
when z<1. INTEGRATIONCONSTANT is inserted only in
integrate(diff(f(z),z)=2/(1-z^2),z).... This behaviour is not stressed
in the manuals, neither is any variable affecting the
inclusion/not-inclusion of INTEGRATIONCONSTANT into indefinite
integration results.
--
Andrei Zorine
>
> No need for fancy ODE machinery. Just iterate INTEGRATE three times,
> being careful with the integration constants. It helps to ASSUME(0<z,
> z<1). And check that it is possible to interchange summation over n
> and the limit for z -> 1-.
>