Results 251 to 260 of about 210,761 (283)

Linear Differential Equations and Logarithmic Derivative Estimates

Proceedings of the London Mathematical Society, 2003
The linear differential equation \[ f^{(k)}+A_{k-1}(z)f^{(k-1)}+\ldots+A_0(z)f=0 \tag{1} \] is considered, where \(A_n(z)\), \(n=0,1,\dots,k-1\), are analytic functions in the unit disk \(\Delta= \{z: | z|
Chyzhykov, Igor, Gundersen, Gary G., Heittokangas, Janne   +2 more
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Extremal Properties of Logarithmic Derivatives of Polynomials

Journal of Mathematical Sciences, 2020
In this paper, some important problems connected with extremal and approximation properties of simple partial rational functions have been studied. It has been proved that for any \(a>1\) the poles of a partial function \(\rho_{n}\) whose sup norm does not exceed \(\ln(1+a^{-1})\) on \([-1,1]\) lie in the exterior of the ellipse with foci \(\pm 1\) and
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The Derivative of the Logarithm

The American Mathematical Monthly, 1916
(1916). The Derivative of the Logarithm. The American Mathematical Monthly: Vol. 23, No. 6, pp. 204-206.
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ON THE LOGARITHMIC DERIVATIVE OF NICHOLSON'S INTEGRAL

Analysis and Applications, 2009
The function [Formula: see text] is studied. By employing uniform asymptotic approximations for Bessel functions, as well as Nicholson's integral for [Formula: see text] and a related integral, uniform asymptotic approximations for Mν(x) are obtained for x → ∞, which taken together are uniformly valid for -∞ < ν < ∞.
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GENERALIZED LOGARITHMIC DERIVATIVE ESTIMATES OF GOL'DBERG–GRINSHTEIN TYPE

Bulletin of the London Mathematical Society, 2003
This paper is devoted to obtaining sharp upper bounds for \(m(r,\frac{f^{(k)}}{f^{(j)}})\), resp. for \(m(r,\frac{\varphi^{(k)}}{\varphi^{(j)}})\), provided \(f\), resp. \(\varphi\), is meromorphic in the complex plane, resp. in the unit disc, and \(k,j\) are integers, \(k>j\geq 0\). These results generalize the logarithmic derivative estimates due to \
Heittokangas, J., Korhonen, R., Rättyä, J.   +2 more
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Logarithmic Derivatives and Generalized Dynkin Operators

2012
Motivated by a recent surge of interest for Dynkin operators in mathematical physics and by problems in the combinatorial theory of dynamical systems, we propose here a systematic study of logarithmic derivatives in various contexts. In particular, we introduce and investigate generalizations of the Dynkin operator for which we obtain Magnus-type ...
Menous, Frederic, Patras, Fr��d��ric   +1 more
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Zeros of higher order logarithmic derivatives

Complex Variables, Theory and Application: An International Journal, 2004
We extend a result of Langley and Shea [J.K. Langley and D. Shea (1998). On multiple points of meromorphic functions. J. London Math. Soc., 57(2), 371–384.] concerning the distribution of zeros of the logarithmic derivative f ′/f to higher order logarithmic derivatives of the form f (k)/f, .
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Logarithmic derivative method and system for capacitance measurement

Review of Scientific Instruments, 2015
A novel method based on logarithmic derivative is introduced to analyze multi-lifetime decay. As the discharge voltage signal of a RC circuit is a special kind of multi-lifetime exponential decay, the logarithmic derivative method can be used to measure single capacitance and multiple capacitances. With the logarithmic derivative method, a log(t) curve
Yichun Wu, Lingzhi Wang, Yuanfeng Cai, Cunqiao Wu   +3 more
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On the integrability of logarithmic derivatives of measures

Mathematical Notes, 1993
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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From the Logarithmic Derivative Lemma to Hayman’s Conjecture

Mediterranean Journal of Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Kai, Liu, Qi
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