# Tagged Questions

139 views

### Inequality of Partial Taylor Series

Hi, For a given $\theta < 1$, and $N$ a positive integer, I am trying to find an $x > 0$ (preferably the smallest such $x$) such that the following inequality holds: \sum_{k=0}^{N} ...
53 views

### Find a bounded function with a supporting point

Given, $g(Z)=\operatorname{tr}\phi(Z)$, where $\phi(Z)= Z^T\left( \operatorname{diag}(ZZ^T\mathbf{1}) - ZZ^T\right) Z$ where $Z$ is a real rectangular matrix with more rows than columns (tall and ...
1k views

### Numerical Computation of arcsin and arctan for real numbers [closed]

I'm coding some numerical methods and I do not know what the correct analysis would be for choosing the implementation for $arcsin$ and $arctan$ for real numbers. Here's what I know: Both functions ...
270 views

### method for getting function from power series/perturbation series

is there any definite method or algorithm,software to get exact function or expression from series.e.g we get series solution of differential equation and we want exact expression rather than ...
2k views

### Why is $\frac{\pi^2}{12}=ln(2)$ not true ?

This question may sound ridiculous at first sight, but let me please show you all how I arrived at the afore mentioned 'identity'. Let us begin with (one of the many) equalities established by Euler: ...