exp1x

exp1x is not a standard mathematical function notation. In many texts, exp denotes the exponential function e^x, with the argument written simply as x. In informal or programming contexts, exp1x may be used as an alias or shorthand for exp(1*x), i.e., e^x. Because multiplication by 1x is just x, exp1x collapses to exp(x) when interpreted this way. However, without an explicit definition in a given source, exp1x is ambiguous and should not be assumed to denote a particular function.

If exp1x is interpreted as exp(x), then it inherits the properties of the exponential function. The derivative of e^x is e^x, and its integral is e^x + C. Its power series expansion is the sum from n = 0 to infinity of x^n/n!, and its domain is all real numbers with range (0, ∞). It is the unique function satisfying f'(x) = f(x) with f(0) = 1, and it appears in a wide range of mathematical and applied contexts, including growth and decay models, compound interest, probability distributions, differential equations, and complex analysis (through expressions like e^{ix}).

In numerical computation, related functions such as expm1(x) are used to compute e^x − 1 with improved precision for small x. Because exp1x is not universally standardized, readers should verify its meaning in any given document or codebase, as it may refer to a different construct in that context.