Expnx

Expnx is a term used in mathematics and computing with several related meanings tied to exponential functions and the expression e^{n x} or iterated exponentials.

Most common interpretation: expnx(n, x) = e^{n x}; in many contexts, it's written as exp(n x). This form arises in scaling of the exponent, modeling growth at rate n with input x.

Another usage: exp_n(x) or exp^n(x) denotes the n-fold iteration of the exponential function, defined by exp_1(x) = e^x and exp_{k+1}(x) = e^{exp_k(x)}. This interpretation is distinct from e^{n x} and is usually treated as a separate family of functions.

Because of the two meanings, properties differ; the first has derivative with respect to x equal to n e^{n x}; the second grows much faster and has domain considerations. In applications, choosing the correct interpretation is important for analysis and modeling.

Example: expnx(2, 3) equals e^6 ≈ 403.4288. By contrast, a corresponding iterated form like exp_3(1) = e^{e^{e}} yields a vastly larger value and presents different mathematical behavior.

See also: exponential function, natural exponential, exp function, iterated exponential.