# Tagged Questions

Questions regarding the Taylor series expansion of univariate and multivariate functions, including coefficients and bounds on remainders. A special case is also known as the Maclaurin series.

40 views

### Taylor series for $g(z)=\frac{(z^2 - 1)}{(z)}$ [closed]

i need to find the Taylor series for $g(z)=\frac{z^2 - 1}{z}$ centered at $z=5$, can somebody help me please? Thanks!! EDITED: The answer must be something like this: Summatory of An(z - 5)^n from ...
50 views

### When is $1-(1-p)^n \sim pn$

Let $0<p=p(n)<1$ with $p=o(1)$. For which $p$ is it true that $1-(1-p)^n \sim pn$? With $\sim$ I mean that they are asymptotically the same, so $\frac{1-(1-p)^n}{pn}\rightarrow 1$, or at least ...
71 views

### Maclaurin Expansion of $\ln(3+x)$

I'm currently evaluating a simple Maclaurin expansion, the confusion I have with is why the expansion of this function is constructed to be: $\ln\left[3\left(1+\dfrac{x}{3}\right)\right]$ as opposed ...
26 views

### Taylor expansions for functions of several variables

I need help with this question. a) Determine the Taylor expansions at the origin up to the square Terms of $f(x, y, z) = \cosh(x) - \sin(yz) - xy(z - 1)^7$ and $g(x, y) = e^{-y}/(1-x^2)$. b) ...
I want to expand, $$(X + Y)^s$$ for $X,Y \geq 0$ and $s \in \mathbb{C}$. Into something of the form, $$\sum_i X^{p_i} Y^{q_i}$$ for $p_i, q_i \in \mathbb{C}$. I am doing this to expand the ...