expFxy
ExpFxy is a shorthand notation used in mathematical contexts to denote the exponential of a two-variable function F, written as exp(F(x,y)) or e^{F(x,y)}. It is not a standardized object with a single definition, but rather a convenient way to reference the quantity when F: R^2 -> R is real-valued and the exponential appears in equations.
If F is real-valued, ExpFxy means e^{F(x,y)}. If F takes complex values, the exponential is still defined
For real-valued F, ExpFxy > 0 for all (x,y) in the domain. Exponential rules apply: ExpFxy · ExpGxy
If F(x,y) = ax + by + c, then ExpFxy = e^{ax+by+c} = e^{c} e^{ax} e^{by}. If F(x,y) = -((x-μ)^2+(y-ν)^2)/(2σ^2), ExpFxy yields
ExpFxy appears in statistics and physics, for example in Boltzmann weights e^{-E(x)} and in the exponential family
Numerical evaluation must manage overflow and underflow; stable techniques include log-exp transforms and the log-sum-exp trick