Transcendental Equation


Also found in: Dictionary, Wikipedia.
Related to Transcendental Equation: Transcendental function

Transcendental Equation

 

an equation containing transcendental functions (for example, exponential, logarithmic, trigonometric, or inverse trigonometric functions) of the unknowns. Examples of transcendental equations are sin x + log x = x and 2x – log x = arc cos x.

References in periodicals archive ?
It is a transcendental equation, and it contains two parameters with unambiguous physical meaning, which can be defined as the ratio of rotary mass moment of inertia and the ratio of the mass, respectively.
Based on Section 2, the transcendental equation can be solved with guided wave propagation theory.
Seeking the answer needs solution of transcendental equation, which can be done with numerical analysis by using computer.
[[beta].sub.m] is mth root of transcendental equation cos ([[beta].sub.m]m x b) = 0
Seeking a closed-form solution (1) to the transcendental equation y[e.sup.y] = x, in terms of y, we are led to the definition for the Lambert W function; it being defined as the inverse of the function f(x) = x[e.sup.x].
(8) To determine the frequency of the isolated DRA using this model, a transcendental equation must be solved.
In violated inequality (14) in some areas (-[alpha], -[[alpha].sub.1]) the contact is broken, then instead [alpha] in (13) it should be taken [alpha] = [[alpha].sub.1] ([beta]), where [[alpha].sub.1] is the root of the transcendental equation
Transcendental equation (29) has infinite number of roots, using the Heavisides sentence (24), where s sn and by utilization of (27), (28) we get the final relation for the non-dimensional concentration field of hydrolyzed protein in the amaranth stalk:
298-305] where it is shown that this problem reduces to the study of the solutions of a single transcendental equation.
Equation (25) for determination of eigenvalues of the solution is a transcendental equation. In order to determine the roots a numerical procedure was used.
[m.sub.n] = [[lambda].sub.n] a / [square root of [alpha]]--as being the root of "n" order of the transcendental equation:
Equating the main determinant of the system to zero, a complex transcendental equation for the wavenumber [Mathematical Expression Omitted] is obtained.

Full browser ?