Transcendental Equation

Related to Transcendental Equation: Transcendental function

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

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 2^x – log x = arc cos x.

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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.

Frequency Equation of Flexural Vibrating Cantilever Beam Considering the Rotary Inertial Moment of an Attached Mass

Based on Section 2, the transcendental equation can be solved with guided wave propagation theory.

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Seeking the answer needs solution of transcendental equation, which can be done with numerical analysis by using computer.

Applications of numerical calculation in engineering design

[[beta].sub.m] is mth root of transcendental equation cos ([[beta].sub.m]m x b) = 0

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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].

A new elementary function for our curricula?

(8) To determine the frequency of the isolated DRA using this model, a transcendental equation must be solved.

Design curves for estimating the resonant frequency and Q-factor for rectangular dielectric resonator antennas

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

Elementary calculation of clip connections with incomplete sweep of shaft

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:

The kinetics of protein enzymatic extraction from the amaranth stalk

298-305] where it is shown that this problem reduces to the study of the solutions of a single transcendental equation.

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Equation (25) for determination of eigenvalues of the solution is a transcendental equation. In order to determine the roots a numerical procedure was used.

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[m.sub.n] = [[lambda].sub.n] a / [square root of [alpha]]--as being the root of "n" order of the transcendental equation:

The analytical model for determining the temperature distribution in transitory regime in piping walls

Equating the main determinant of the system to zero, a complex transcendental equation for the wavenumber [Mathematical Expression Omitted] is obtained.

Frequency-independent waveguide attenuator with a resistive film in the diagonal plane