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periodic_argument does currently leave unevaluated all expressions that contain periodic_argument, atan2, arg or atan after simplifications. It follows that the following expression will often appear in the convergence conditions of integrals computed by meijerint. >>> unbranched_argument(1/polar_lift(x)) periodic_argument(1/polar_lift(x), oo) >>> meijerint.meijerint_definite(exp(I*t*x)/(x + a), x, 0, oo) (exp(-I*a*t)*expint(1, a*t*exp_polar(-I*pi/2)), ((Abs(periodic_argument(1/polar_lift(a), oo)) < pi) & Eq(Abs(periodic_argument(exp_polar(-I*pi/2)*polar_lift(t), oo)), pi/2)) | ((Abs(periodic_argument(1/polar_lift(a), oo)) < pi) & (Abs(periodic_argument(exp_polar(-I*pi/2)*polar_lift(t), oo)) < pi/2)) | ((Abs(periodic_argument(exp_polar(-I*pi/2)*polar_lift(t), oo)) < pi/2) & ((Abs(periodic_argument(1/polar_lift(a), oo)) < pi) | ((Abs(periodic_argument(1/polar_lift(a), oo)) < pi) & Ne(Abs(periodic_argument(1/polar_lift(a), oo)), pi))))) These expressions will be more readable if periodic_argument is allowed to return values containing arg. >>> unbranched_argument(1/polar_lift(x)) -arg(x) >>> meijerint.meijerint_definite(exp(I*t*x)/(x + a), x, 0, oo) (exp(-I*a*t)*expint(1, a*t*exp_polar(-I*pi/2)), ((Abs(arg(a)) < pi) & Eq(Abs(arg(t) - pi/2), pi/2)) | ((Abs(arg(a)) < pi) & (Abs(arg(t) - pi/2) < pi/2)) | ((Abs(arg(t) - pi/2) < pi/2) & ((Abs(arg(a)) < pi) | ((Abs(arg(a)) < pi) & Ne(Abs(arg(a)), pi)))))
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