Meaning of logarithmic derivative | Babel Free

Definitions

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.

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.”

“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.”

“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.”

CEFR level