Transcendental Function


Also found in: Dictionary, Wikipedia.

Transcendental Function

 

an analytic function that is not algebraic. Simple examples of transcendental functions are exponential functions, trigonometric functions, and logarithmic functions.

If transcendental functions are treated as functions of a complex variable, a characteristic feature of a transcendental function is the existence of at least one singularity other than poles and branch points of finite order (seeSINGULAR POINT). For example, e2, cos z, and sin z have the essential singularity z = ∞, and In z has branch points of infinite order at z = 0 and z = ∞.

The foundations of the general theory of transcendental functions are provided by the theory of analytic functions. Special transcendental functions are studied in the corresponding disciplines—for example, the theory of hypergeometric functions, the theory of elliptic functions, or the theory of Bessel functions.

REFERENCE

Whittaker, E. T., and G. N. Watson. Kurs sovremennogo analiza, 2nd ed., parts 1–2, Moscow, 1969. (Translated from English.)
References in periodicals archive ?
In Agamben's variant of this kind of thinking, then, the transcendental function is supplied by a "zone of indeterminacy" which, for him, harbours the promise of suspending the violences that have been enabled by it.
In the same way, specific psychological mechanisms that realize a transcendental cognitive function can be studied only empirically, even though a highly abstract description of the basic temporal-causal processes that realize the transcendental function can be achieved by philosophical reflection.
The series expansion for many transcendental functions can be obtained from the Maclaurin's series.
Another aspect of mathematics worth investigating visually is the behavior of mathematical expressions known as transcendental functions (SN: 5/26/84, p.328).
Moreover, it is the first and only elementary transcendental function that provides a nontrivial example of branching behaviour on the real domain.
For simple transcendental functions, the error varies between 0 and 70 percent of the gradient across the polygon.
Calculus: Early Transcendental Functions, 7th Edition
Zhir, "On the best polynomial approximation of entire transcendental functions of generalized order," Ukrainian Mathematical Journal, vol.
Among the topics are introduction to analytic geometry, the integral and its applications, derivatives of transcendental functions, integration techniques, infinite series, higher-order linear differential equations, and the Laplace transform.
The transcendental functions defined by six second-order nonlinear equations are called as Painleve transcendent.
On the Zeros of Some Elementary Transcendental Functions. Izvestiya Akademii Nauk SSSR, Vol.

Full browser ?