Transcendental equation Definition and 17 Threads

A transcendental equation is an equation containing a transcendental function of the variable(s) being solved for. Such equations often do not have closed-form solutions. Examples include:








x



=

e

−
x






x



=
cos
⁡
x





2

x





=

x

2








{\displaystyle {\begin{aligned}x&=e^{-x}\\x&=\cos x\\2^{x}&=x^{2}\end{aligned}}}

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  1. J

    What is the Correct Approach to Solving the Deuteron Transcendental Equation?

    Dear Forum, I am trying to solve a problem (4.6) from the introductory nuclear physics textbook by Krane. The problem is as follows: Solving the deuteron using the radial equations gives the transcendental function, ##k_{1} \cot{k_{1}R} = -k_{2}## Were ##k_{1} =...
  2. H

    Mathematica Find all values of E for a transcendental equation

    Hi, I'm trying to solve a transcendental equation. I would like all the values of E that solve this equation. ##k = -l \cdot Cot(la)## However, using Nsolve or FindRoot, they give me a precision error. Hence, I'm trying this form. ##\sqrt{-e /(e+v)} = -Cot(la)## FindRoot only give me an...
  3. J

    I Error Propagation in Transcendental Equation

    Hey guys, I'm in a class where we're learning about waveguides, and without going into too much depth, we often solve an equation $$ \tan{(\kappa (\frac{a}{2}))} = \frac{\gamma}{\kappa} $$ for ##\kappa## numerically since there isn't an analytic solution for ##\kappa##. I'm doing a project...
  4. Automata-Theory

    A Particle Moving Along a Ring with Variable Potential

    Homework Statement Alrighty, so here's my problem in a nutshell: Some particle of mass m is confined to move along a ring of radius R. Since it's on a ring, it has periodic boundary conditions--i.e.: For the boundary defined as ##-\pi R \leq x \leq \pi R##, ## x = -\pi R ## and ## x = \pi R...
  5. E

    What is the solution for the attached equation?

    Good afternoon, i was just wondering if this equation is possibly solvable where I(z) is a function of z. The equation is: I(z)=cosh(1/2 ∫I(z)dz) I know it looks stupid but is it possible? How would you approach this problem? Thank you.
  6. D

    Transcendental equation problem

    i have a transcendental equation and i have not a mathematique superieur formation ( I'm an hydraulic engeneer) and i want to resolve it but i can't so if you can help me with it ! the equation is : 2*x*n*ctg(2x)= x2 - n2 or (same equation)...
  7. Monsterboy

    Is there a solution to this transcendental equation ?

    This is not a homework problem, this equation simply occurred to my mind and my math teacher said such an equation either can't exist or he doesn't know the answer. sinX ➕ cosX = lnX I don't know how to start...
  8. U

    Transcendental equation from a finite square well potential

    if I have a transcendental equation such as this one: tan(l a) = -l / sqrt (64/a^2 - l^2 ) Where l=sqrt(2m(E+V) /hbar^2 ) and 'a' is the width of a finite square well, how can I solve this equation in terms of both l and a. I have successfully graphed the two sides of the equation...
  9. S

    Solving a Transcendental Equation Using a Numerical or Graphical Method

    Homework Statement I have this equation: y = 5(1 - e-x) and I need to find its root. Homework Equations I'm trying to go from Planck's blackbody formula to wien's displacement law by taking the derivative of Planck's blackbody formula with respect to wavelength and then setting it...
  10. kq6up

    Does this example give a transcendental equation?

    I am teaching AP Physics, and wrote a problem on the board as an example of how to attack a problem. I new the answer would be nasty, but I didn't actually want them to solve it. I only wanted them to reduce the problem to one e.q. and one unknown. I was wondering if there is an analytic...
  11. S

    How do I solve a transcendental equation?

    Can anyone tell me how can i find a solution to a transcendental equation? Any link, where i will get methods to solve them? Thank you..
  12. G

    Solving a transcendental equation

    Suppose you have the equation x^2*(log x)^{1/3}=-C for very small C. I have a book claims that asymptotically, for very small C, the solution is: x^2=C*\frac{2}{[logC]^{1/3} } I'm not quite sure how to show this. If the 2 wasn't there, it looks like what they did was: x^2=-\frac{C}{(log...
  13. S

    Understanding Transcendental Equations in Multicompartment Systems

    Hi, I am reading a paper where part of the solution to an equation of diffusion in a multicompartment system includes the "sum of all nonnegative roots kj of the following transcendental equation, 2*u*(cos(k)-cos(q))-k*sin(k) = 0. Then the authors of the paper say: "Note that the...
  14. M

    Eigenvalue solutions of the transcendental equation

    Homework Statement Given the Sturm-Liouville system: y'' + λy = 0 , y(0) - y'(0) = 0 , y(1) + y'(1) = 0 Show using the Rayleigh Quotient that the eigenvalues are positive. Show that these eigenvalues are given as the solutions of the transcendental equation: tan ( √λ ) =...
  15. A

    Possible analytical solution of transcendental equation by an assumption.

    Is it possible to solve the next transcendental equation analytically (obviously for k): sinh(k)=(b/2)(1+(e^(-2kl))) making the assumption that (bl >>1). I think that is not possible, but in an article that i found, they solve it by making that assumption, and they reach to the solution...
  16. G

    Solving transcendental equation- Quantum Mechanics

    I don't know if I am being dumb or not but I need to solve a transcendental equation numerically and I need to write a program that can do this. The equation is so I can find the the ground state energy of a wave function in a semi-infinite well. I was told to use the Newton-Raphson method to...
  17. T

    Is There an Analytical Solution to the Transcendental Equation x = cot(x)?

    Hi, can somebody see if there is a way to solve this analytically? x = \mbox{cotg } x I know it could be solved numerically, but I'm interested in analytical solution only (if it exists, of course). Thank you very much.
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