# 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.

526 views

### Lagrange remainder vs. Alternating Series Estimation Theorem: do they always give you the same error bound?

Given a function and its nth degree Taylor series approximation, we can use the Lagrange form of the remainder to get a maximum value of the error of approximation. If the series is also an ...
33 views

### Asymptotic expansion of elliptic integral

I am trying to find the first 2-3 terms of the asymptotic expansion in terms of 1/ρ of the elliptic integral I_n(\rho)=\int_0^\frac{h_2}{\rho}\frac{t^{2n}/h_2^{2n}}{(E_n(t))^2\...
31 views

Is there a formula to multiply many series (More than two) using the Cauchy product? If there isn't, please tell me how I can write this formula $\left( \frac{1}{a-e^x} \right) ^{n+1}$as the ...
32 views

### Prove that this limit is the logarithmic derivative of the Riemann zeta function.

Prove the following limit: $$-\frac{\zeta '(s)}{\zeta (s)}=\lim_{c\to 1} \, \left(\frac{\zeta (c) \zeta (s)}{\zeta (c+s-1)}-\zeta (c)\right)$$ As a starting point I tried to enter this series ...
38 views

68 views

### Convergence of the series $\sum \frac{(-1)^{n}}{n^{\frac{2}{3}}+n^{\frac{1}{3}}+(-1)^{n}}$

To prove that nature of the following series : $$\sum \dfrac{(-1)^{n}}{n^{\frac{2}{3}}+n^{\frac{1}{3}}+(-1)^{n}}$$ they use in solution manual : My questions: I don't know how to achieve ( * ) ...
29 views

### Difference/switch between big/small o in taylor series

for example i only know taylor series with small o is there anyway to switch from small o to big o in taylor series and why when we want to see the nature of some series we use taylor series with ...
65 views

### Can the series $\sum_{n=0}^\infty \frac{(-1)^n}{\sqrt{2^n n!}} x^{n}$ be summed? [closed]

Can the following series $$\sum_{n=0}^\infty \frac{(-1)^n}{\sqrt{2^n n!}} x^{n}$$ be summed?
28 views

### Find the Taylor-series expansion of a square of a rational function of a complex variable

I've been trying to find the Taylor-series expansion of the following function: $$f(z)=\left ( \frac{1+z}{1-z} \right )^2$$ az the origin : Z0 = 0. also I would like to find the region of ...
29 views