Let $h(x)$ be a holomorphic complex function. Is it true that the ratio :$h'(x)/h(x)$ is holomorphic as well? (please explain why)
2026-03-29 02:37:02.1774751822
the ratio of the derivative of a holomorphic function over itself
56 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in COMPLEX-ANALYSIS
- Minkowski functional of balanced domain with smooth boundary
- limit points at infinity
- conformal mapping and rational function
- orientation of circle in complex plane
- If $u+v = \frac{2 \sin 2x}{e^{2y}+e^{-2y}-2 \cos 2x}$ then find corresponding analytical function $f(z)=u+iv$
- Is there a trigonometric identity that implies the Riemann Hypothesis?
- order of zero of modular form from it's expansion at infinity
- How to get to $\frac{1}{2\pi i} \oint_C \frac{f'(z)}{f(z)} \, dz =n_0-n_p$ from Cauchy's residue theorem?
- If $g(z)$ is analytic function, and $g(z)=O(|z|)$ and g(z) is never zero then show that g(z) is constant.
- Radius of convergence of Taylor series of a function of real variable
Related Questions in HOLOMORPHIC-FUNCTIONS
- order of zero of modular form from it's expansion at infinity
- Holomorphic domain of $ \Phi\left(z\right)=\ln\left(\frac{z-a}{z+a}\right)$
- Complex Analysis - Harmonic function as real part of holomorphic function
- Impossibility of conformally mapping graph of $x\sin(1/x)$ to $\mathbb{R}$
- Product of holomorphically convex spaces is again holomorphically convex
- Prove that $X$ is a Riemann surface using basic definitions
- $B=\{t\in[-T,T]:|f(\sigma+it)|>\ell\}$, does it hold that $|B|>\epsilon 2T$
- Show that $|f(0)| \leq \frac{1}{4}$ for every holomorphic function $f:\Bbb D \to \Bbb D$ such that $|f(\frac{1}{2})|+|f(-\frac{1}{2})|=0$
- Proving $0$ is a removable singularity
- Holomorphic function satisfying $f^{-1}(\Bbb R)=\Bbb R$ is of the form $f(z)=az+b$
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
It won't necessarily be a holomorphic function. Actually, anywhere $h(x)=0$ it wont be holomorphic.
For example for $h(x)=x$, $h^{'}(x)/h(x) = 1/x$ which is not holomorphic at $x=0$.
It will be a meromorphic function tho