Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 84

prove that $f(x)=sum_{|alpha|leq k}frac{1}{alpha !}D^{alpha}f(0)x^{alpha} + O(|x|^{k+1})$

If $alpha$ is multiindex and $f$ is smooth,prove that $f(x)=sum_{|alpha|leq k}frac{1}{alpha !}D^{alpha}f(0)x^{alpha} + O(|x|^{k+1})$. The hint is to use taylors form for $g(t)=f(tx)$. If i do...

Asked on 11/16/2021 by weymar andres

1 answer

Calculate $sum_{r=0}^n cosh(alpha+2rbeta)$

I try to calculate $sum_{r=0}^ncos(alpha+2rbeta)$ first to get some insights. First we prove that $sum_{r=0}^inftycos(alpha+2rbeta)=0$. (The statement and the proof is flawed, I will edit it later.) ...

Asked on 11/16/2021

1 answer

Analytic continuation of a function on the right half-plane to a region enclosing the circle ${ lvert z rvert = 3}$

I am trying to solve the following question: Show that there exists an analytic function $f$ in the open right half-plane such that $(f(z))^2 + 2f(z) equiv z^2$....

Asked on 11/16/2021 by qpca

0 answer

Show that $sum_n (1-e^{-1/n})$ diverges

I'm stuck in showing that $sum_n (1-e^{-1/n})$ diverges. The ratio and the root test are inconclusive. Possibly the comparison test is the way to go, but I can't find...

Asked on 11/14/2021

2 answer

Showing the support of a sheaf may not be closed (Liu 2.5)

This is question 2.5 of Qing Liu. I am new in algebraic geometry and really stuck on it and can't do anything to solve it. The question:Let $F$...

Asked on 11/14/2021 by user468730

3 answer

What is the condition for two extreme points?

I am new to the topic of extreme point and trying to get the whole picture. Now I know the extreme theorm that mentions two condition to obtain a critical...

Asked on 11/14/2021 by Mai Ehab

1 answer

Newton's evaluation of $1 + frac{1}{3} - frac{1}{5} - frac{1}{7} + frac{1}{9} + frac{1}{11} - cdots$

How might have Newton evaluated the following series? $$sqrt{2} , frac{pi}{4} = 1 + frac{1}{3} - frac{1}{5} - frac{1}{7} + frac{1}{9} + frac{1}{11} - cdots$$ The method of the...

Asked on 11/14/2021 by Robert Bell

3 answer

Proving that $g_nf_n$ converges to $0$ in measure on $[0,1]$

Question: Let $f_n,g_n:[0,1]rightarrow [0,infty)$ be measurable functions. Assume $f_nrightarrow 0$ in measure on $[0,1]$, and that $int g_ndx<1$ for all $ninmathbb{N}$. Prove that...

Asked on 11/14/2021 by User7238

2 answer

Every h-cobordism embeds into $M times I$?

Suppose we are in high dimension. By the s-cobordism theorem, any h-cobordism has an inverse given by a h-cobordism with the inverse torsion. Thus we have a isomorphism from the...

Asked on 11/14/2021 by Connor Malin

0 answer

The number of types on a set is equal to $binom{n + m - 1}{m - 1}$?

Let $M = {1,2,..., m }$ be a finite set. Consider an $n$-type distribution $t$ on $M$ such that for any $e in M$, ...

Asked on 11/14/2021 by ironX

1 answer

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