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Transcendental equation

About: Transcendental equation is a(n) research topic. Over the lifetime, 1984 publication(s) have been published within this topic receiving 40023 citation(s). more


Open accessBook
01 Jan 1954-
Topics: Daniell integral (79%), Dirichlet integral (74%), Singular integral (74%) more

4,736 Citations

Journal ArticleDOI: 10.1103/PHYSREV.130.1605
Elliott H. Lieb1, Werner Liniger1Institutions (1)
15 May 1963-Physical Review
Abstract: A gas of one-dimensional Bose particles interacting via a repulsive delta-function potential has been solved exactly. All the eigenfunctions can be found explicitly and the energies are given by the solutions of a transcendental equation. The problem has one nontrivial coupling constant, γ. When γ is small, Bogoliubov’s perturbation theory is seen to be valid. In this paper, we explicitly calculate the ground-state energy as a function of γ and show that it is analytic for all γ, except γ=0. In Part II, we discuss the excitation spectrum and show that it is most convenient to regard it as a double spectrum—not one as is ordinarily supposed. more

Topics: Bose gas (58%), Transcendental equation (55%), Perturbation theory (55%) more

2,053 Citations

Open accessBook
01 Jun 1970-
Abstract: Part I. Fundamental Methods: 1. The calculation of functions 2. Roots of transcendental equations 3. Interpolation - and all that 4. Quadrature 5. Ordinary differential equations - initial conditions 6. Ordinary differential equations - boundary conditions 7. Strategy versus tactics - roots of polynomials 8. Eigenvalues I 9. Fourier series Part II. Double Trouble: 10. Evaluation of integrals 11. Power series, continued fractions, and rational approximations 12. Economization of approximations 13. Eigenvalues II - rotational methods 14. Roots of equations - again 15. The care and treatment of singularities 16. Instability in extrapolation 17. Minimum methods 18. Laplace's equation - an overview 19. Network problems. more

667 Citations

Open access
Shigui Ruan, Junjie Wei1Institutions (1)
01 Dec 2003-
Abstract: In this paper, we first establish a basic theorem on the zeros of general transcendental functions. Based on the basic theorem, we develop a decomposition technique to investigate the stability of some exponential polynomials, that is, to find conditions under which all zeros of the exponential polynomials have negative real parts. The technique combines the D-decomposition and τ -decomposition methods so that it can be used to study differential equations with multiple delays. As an application, we study the stability and bifurcation of a scalar equation with two delays modeling compound optical resonators. more

663 Citations

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Topic's top 5 most impactful authors

S.M. Perovich

12 papers, 170 citations

Randhir Singh

11 papers, 223 citations

Leon M. Tolbert

9 papers, 1.3K citations

Olena O. Bulatsyk

7 papers, 13 citations

Jitendra Kumar

7 papers, 168 citations

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