logarithmic derivative
English
editNoun
editlogarithmic derivative (plural logarithmic derivatives)
- (calculus, mathematical analysis) Given a real or complex function , the ratio of the value of the derivative to the value of the function, , regarded as a function.
- 1955, Frank S. Ham, “The Quantum Defect Method”, in Frederick Seitz, David Turnbull, editors, Solid State Physics, Volume 1, Academic Press, page 138:
- From this Coulomb function, we can then calculate the logarithmic derivative of at the eigenvalue for any value of outside the core. If there exists a radius lying in the Coulomb region and sufficiently small that the logarithmic derivative at is a smooth function of the energy, we can obtain the logarithmic derivative for arbitrary energies within a reasonable range by interpolating it between the eigenvalues.
- 1994, Bjarne S. Jensen, The Dynamic Systems of Basic Economic Growth Models, Kluwer Academic, page 329:
- In economics, it is popular to consider the logarithmic derivative , as a convenient growth measure.
- 1995, Philip G. Burke, Charles J. Joachain, Theory of Electron-Atom Collisions: Part 1: Potential Scattering, Plenum Press, page 86:
- In this section we consider the R-matrix method in which a solution is first found in an inner region 0 ≤ r ≤ a by expanding in a basis set yielding the logarithmic derivative of the wave function on the boundary r = a.
Usage notes
edit- The logarithmic derivative can be interpreted intuitively as the infinitesimal relative change in at any given point.
- If is a differentiable function of a real variable and takes only positive values (so that is defined), the chain rule applies and the logarithmic derivative is equal to the derivative of the logarithm: .
- The definition above is more broadly applicable: for a function of a complex variable, its logarithmic derivative will be computable so long as and is defined.
Translations
editratio of the value of the derivative to the value of the function, regarded as a function
Further reading
edit- Logarithmic differentiation on Wikipedia.Wikipedia