Ok, I know this question is cheese! But I am stuck at this for the past two hours. Getting different answers after the expansion. Here's what I know: $1/(1-z) = -1/z -1/z^2 - \cdots$ valid for $|z|>1$. This series will be used.
2026-04-01 16:29:49.1775060989
What is the expansion of $1/(15+5z)$ valid for $|z|>3$?
42 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 LAURENT-SERIES
- Find Laurent series of rational function $f(z)={1 \over (z+1)^2(z+2)}$
- How do I show with Laurent Series Expansion that $1/z$ has a simple pole for $z=z_0=0$?
- Order of Poles of $1/\cos(1/z)$
- Classification of singularities of $\sin\left( \frac{1}{\sin(\frac{1}{z})}\right)$
- Laurent expansion and singularities of $\frac{1-\cos(z)}{e^{2iz}-1}$
- Laurent Series problems
- Laurent series VS Fourier series.
- Laurent series and radius of convergence of $f(z)=\frac{1}{(1-\cosh z)^2}$
- Show that a localization a power series ring $R[[x]]$ by $S$ can be written a certain way.
- Laurent series of complex function
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?
Write $$\frac{1}{15+5z} = \frac{1}{15} \frac{1}{1+\frac{z}{3}} = \frac{1}{15} \frac{1}{1-\frac{-z}{3}}$$