Transcendental equation
From Wikipedia, the free encyclopedia
A transcendental equation is an equation containing a transcendental function. Examples of such an equation are
- x = ex
- x = sin(x)
[edit] Solution methods
Some methods of finding solutions to a transcendental equation use graphical or numerical methods. For a graphical solution, one method is to set each side of a single variable transcendental equation equal to a dependent variable (for example, y) and plot the two graphs, using their intersecting points to find solutions. The numerical solution extends from finding the point at which the intersections occur using some kind of numerical calculations (calculator or math software). Approximations can also be made by truncating the Taylor series if the variable is considered to be small. Additionally, Newton's method could be used to solve the equation.
Often special functions can be used to write the solutions to transcendental equations in closed form. In particular, the first equation has a solution in terms of the Lambert W Function.
