China
Africa
Explore chapters and articles related to this topic
Chapter S4: Special Functions and Their Properties
Published in Andrei D. Polyanin, Valentin F. Zaitsev, Handbook of Ordinary Differential Equations, 2017
Andrei D. Polyanin, Valentin F. Zaitsev
where n = 0, 1, 2, . . . (the last sum is dropped for n = 0), ψ(z)=[lnΓ(z)]z′ $ \psi (z) = [ {\text{ln }}\Gamma (z)]_{z}^{'} $ is the logarithmic derivative of the gamma function,
Existence Theorems and Special Functions
Published in L.M.B.C. Campos, Singular Differential Equations and Special Functions, 2019
The digamma function (9.460a) is defined as the logarithmic derivative of the gamma function: ψν≡ddνlogΓν=Γ′νΓν:Γ′ν=ψνΓν,1Γν′=−Γ′νΓν2=−ψνΓν,
L
Published in Splinter Robert, Illustrated Encyclopedia of Applied and Engineering Physics, 2017
[computational, nuclear] Mathematical mechanisms used to solve for wave-functions at boundary conditions. The logarithmic derivative transforms a function to the ratio of the function’s derivative and the function itself: log10 10 = 1. At boundaries both the function and the first derivative are required to be continuous and hence this function provides the ideal approach. The solution will still require normalization/scaling.
Estimating a pressure dependent thermal conductivity coefficient with applications in food technology
Published in Inverse Problems in Science and Engineering, 2020
Marcos A. Capistrán, Juan Antonio Infante del Río
Note that hypothesis (H5) means an upper estimate of the logarithmic derivative of k. Then, taking in account the positivity of k, we write In order to discretize u, we shall use an equidistant grid on interval and the finite element basis of piecewise linear functions on such that (Kronecker delta). We assume that and we want to determine for ( is known).
A central limit theorem for periodic orbits of hyperbolic flows
Published in Dynamical Systems, 2021
Stephen Cantrell, Richard Sharp
In fact, it will be convenient to work with the logarithmic derivative (with respect to s) . Write for a set of all (not necessarily prime) periodic orbits of and, for , if , , with , write . Then we have whenever the series converges.
Globally convergent differentiators with variable gains
Published in International Journal of Control, 2018
The logarithmic derivative of L0 is assumed to be bounded, for some known M. It is also assumed that the noises η(t), ηL(t) are not large compared with L0(t), |η(t)| ≤ ϵL0(t), |ηL(t)| ≤ ϵLL0(t), ϵL < 1, where the constant parameters ϵ, ϵL are considered unknown.