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The normality of the logarithmic derivative

open access: yesThe normality of the logarithmic derivative
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Deriving Phase from Logarithmic Gain Derivatives

Circuits, Systems & Signal Processing, 2002
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Rusu, Corneliu   +2 more
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Newq-derivative andq-logarithm

International Journal of Theoretical Physics, 1994
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Chung, Ki-Soo   +3 more
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Logarithmic derivatives of theta functions

Israel Journal of Mathematics, 2005
The authors give two new proofs of the identity \[ \sum_{n=0}^\infty \delta(3n+1)x^n= \prod_{n=1}^\infty \frac{(1-x^{3n})^3} {(1-x^n)} \] where \(\delta(n)= d_1(n)- d_2(n)\) is the number of divisors of \(n\) congruent to \(i\bmod 3\). The main tool of the proofs is the theory of theta functions with characteristics: \[ \theta\biggl[ {{\varepsilon ...
Farkas, Hershel M., Godin, Yves
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On the Growth of the Logarithmic Derivative

Computational Methods and Function Theory, 2001
Let \(f\) be a meromorphic function on \(\mathbb{C}\) with \(f(0)=1\). \textit{A. Gol'dberg} and \textit{V. Grinshtein} [Math. Notes 19, 320-323 (1976; Zbl 0338.30020)] sharpened the lemma of logarithmic derivative in Nevanlinna theory as follows: \[ m\left(r,\frac{f'}{f}\right)\leq \log^+\frac{\rho T(\rho,f)}{r(\rho-r)}+ c, \] where \(\rho>r\), \(c ...
Benbourenane, Djamel, Korhonen, Risto
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LOGARITHMIC VERSION OF INTERPOLATION INEQUALITIES FOR DERIVATIVES

Journal of the London Mathematical Society, 2004
The classical Gagliardo-Nirenberg inequality \[ \| \nabla^{(k)} u \| _q \leq C \, \| u \| ^{1-k/m}_r \| \nabla^{(m)} u \| ^{k/m}_p \] in \(R^n ...
Kałamajska, Agnieszka   +1 more
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