expb

Expb is a term encountered in mathematics and related fields that does not have a single universal definition. In many contexts it refers to the exponential function evaluated at the parameter b, most often written as exp(b) or e^b. The function exp satisfies exp'(b) = exp(b) and has the Maclaurin series exp(b) = sum from n=0 to infinity of b^n/n!. It maps real or complex inputs to positive real or complex outputs and is the inverse of the natural logarithm.

Expb is central to models of growth and decay, compound interest, and the solution of linear differential equations. It also appears in probability theory, including the exponential distribution and in the exponent of the densities of many distributions through the exponential family. When the exponent is linear in parameters, as in exp(b^T x), exp is used to enforce positivity and encode multiplicative effects.

In computing, exp is the standard function name in many programming languages for computing e^x, though the exact syntax differs between languages. The symbol expb is not a universally standardized function name; in some texts it may be used as a placeholder for exp(b) or as a label for an auxiliary exponential parameter in a model. When encountering expb, it is best to consult the specific notation of the source to determine its intended meaning.

See also: exponential function, base e, natural exponential, e^x, exp, exponential growth, exponential distribution, exponential family.