The Todd function T(x) has the property that T(x) equals T(-x) times this function of x.  Lindemann's theorem states that performing this function on a set of linearly independent algebraic numbers results in a set of algebraically independent numbers, and Nesterenko proved the algebraic independence of (*) π and this function of π.  It is equal to the sum of the secant of the Gudermannian and the tangent of the Gudermannian, or the sum of the hyperbolic sine and hyperbolic cosine.  In electrical engineering, phasors make use of the Euler formula, which states that this function of iθ is equivalent to cis θ.  It is the only nonzero function that equals its own deriva
The Todd function T(x) has the property that T(x) equals T(-x) times this function of x.  Lindemann's theorem states that performing this function on a set of linearly independent algebraic numbers results in a set of algebraically independent numbers, and Nesterenko proved the algebraic independence of (*) π and this function of π.  It is equal to the sum of the secant of the Gudermannian and the tangent of the Gudermannian, or the sum of the hyperbolic sine and hyperbolic cosine.  In electrical engineering, phasors make use of the Euler formula, which states that this function of iθ is equivalent to cis θ.  It is the only nonzero function that equals its own derivative.  For 10 points, name this function whose inverse is the natural log.
The Todd function T(x) has the property that T(x) equals T(-x) times this function of x.  Lindemann's theorem states that performing this function on a set of linearly independent algebraic numbers results in a set of algebraically independent numbers, and Nesterenko proved the algebraic independence of (*) π and this function of π.  
(natural) {exponential} function [accept things like {exponentiation} with base e; accept {e to the x} or really anything starting with {e to the} (some argument)] (1) [DW]