argSxy
argSxy is a notation used to denote the argument, or phase angle, of a complex-valued quantity S evaluated at a pair of real variables x and y. When S is a function of two real variables and takes complex values, it can be written as S(x,y) = u(x,y) + i v(x,y), where u and v are real-valued. The argument represents the angle of the complex number S(x,y) in the complex plane and is commonly defined as argSxy = atan2(v(x,y), u(x,y)). The principal value of the argument typically lies in the interval (-π, π], but in general the argument is multivalued, taking the form θ + 2kπ for any integer k.
In practice, argSxy is used to describe the phase of a two-variable complex surface. It is undefined
Applications of argSxy appear in fields such as wave physics, optics, and signal processing, where the phase
Notes: the exact notation argSxy is not universally standardized; some texts use Arg S(x,y) or refer to