logarithmic derivative
noun1
Calculus, Mathematical analysis, Mathematics, Sciences Given a real or complex function f, the ratio of the value of the derivative to the value of the function, (f')/f, regarded as a function.
- From this Coulomb function, we can then calculate the logarithmic derivative of U²(r) at the eigenvalue for any value of r outside the core. If there exists a radius R lying in the Coulomb region and sufficiently small that the logarithmic derivative at R 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.1955, Frank S. Ham, “The Quantum Defect Method”, in Frederick Seitz, David Turnbull, editors, Solid State Physics, Volume 1, Academic Press, page 138:
- In economics, it is popular to consider the logarithmic derivative (#92;ln#92;varphi(t))'#61;#92;varphi'(t)#47;#92;varphi(t), as a convenient growth measure.1994, Bjarne S. Jensen, The Dynamic Systems of Basic Economic Growth Models, Kluwer Academic, page 329:
1 more example
- 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.1995, Philip G. Burke, Charles J. Joachain, Theory of Electron-Atom Collisions: Part 1: Potential Scattering, Plenum Press, page 86: