On the Exact Analytical Solutions of Certain Lambert Transcendental Equations

Abstract

The subject matter of this paper is the Special Trans Functions Theory (STFT) in finding the exact analytical closed form solutions (the new special tran functions) of certain Lambert transcendental equations. Note that these Lambert transcendental equations frequently appear in applied physics and engineering domain. The structure of the theoretical derivations, proofs, and numerical results confirms validity and basic principles of the STFT. Undoubtedly, the proposed exact analytical approach implies the qualitative improvements of the conventional methods and techniques.

Concerning an analytical solution of some families of Kepler’s transcendental equation

“…5 polynomialization of Kepler's equation through Chebyshev polynomial expansion of the sine is presented. , Hopfield neuron analysis 14 some families of transcendental equations, 8,12,15,20,[23][24][25]38 solar cell analysis, 16,21,35 Plutonium temperature estimation, 8,17,36 ambient temperature estimation, 18,11 Lambert transcendental equations analysis, 8,20 as well as in problem in engineering materials, 22,34,40,41 ect. The biggest impact of this work is in the usage of a new STF theory approach in formulae genesis for the determining position (r, v) in time t. All investigations and analysis of the value E in this paper have been consistently accomplished with the usage of STF theory.…”

“…[8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]34,35 The Kepler's transcendental equation for determining the eccentric anomaly in celestial mechanics (1) after some symbolic modification of the type…”

The Special Trans Functions Theory for the Degree of Nuclear Fuel Burn-Up Estimation

“…(3)) is solvable using the Special Tran Function Theory [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Let us note that Perovich's Special Tran Functions Theory (STFT), has been proved to be a very powerful theory for solving transcendental equations, some integral and integro-differential equations, and, obtaining exact analytical closed-form solutions.…”

“…Let us note that Perovich's Special Tran Functions Theory (STFT), has been proved to be a very powerful theory for solving transcendental equations, some integral and integro-differential equations, and, obtaining exact analytical closed-form solutions. Examples of STFT application are shown in articles concerning the closed-form solution genesis in: the theory of neutron slowing down [ [6], [7], [16]], the nonlinear circuit theory [ [8], [16], [22]], the linear transport theory [ [9], [16], [20]], the Hopfield neuron analysis [11], some families of transcendental equations analysis [ [12], [16], [17]], the solar cell theoretical analysis [ [13], [18], [22]], the Plutonium temperature estimation [14], the ambient temperature estimation [ [15], [16]], the Lambert transcendental equations analysis [ [16], [17], [23]], as well as in the problem in the engineering materials [19], [21], [22]], etc.…”

Obtaining an analytical STFT closed form solution to the solar cell junction ideality factor using the maximum power point characteristics

“…In this section, the subject matter is the problem of finding an exact analytical closed -form solution to the Lambert transcendental equation for diode quality factor n, using the Special Trans Functions Theory ( [20], [23]). For convenience we restrict ourselves to the transcendental equation given in the section II, Eq.…”