logarithmic derivative

plural logarithmic derivatives

1. calculusGiven 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.

   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

   2 more examples

   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 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