I am intending to know some of the open problems on integrals,series and number theory with rewards. Also if there is any site to earn small monetary rewards by solving mathematical problems.Read more
I am intending to know some of the open problems on integrals,series and number theory with rewards. Also if there is any site to earn small monetary rewards by solving mathematical problems.Read more
$ T$ is an algebraic polynomial $ $ T=p_0(x) + p_1(x) \cdot y + p_2(x)\cdot y^2 + \cdots + p_n(x)\cdot y^n $ $ $ p_i(x)$ is polynomial with rational coefficients. When $ T=0$ , or $ $ p_0(x) + p_1(x) \cdot y + p_2(x)\cdot y^2 + \cdots + p_n(x)\cdot y^n =0$ $ $ $ y=\theta\left(Read more
I am interested in the series $ $ \sum_{n\geq 1}I_n(x)\lambda^n$ $ which is not the full generating series of the modified Bessel function of the first kind because it start from $ n=1$ and not at $ -\infty$ . If we can not find a closed form for this series, what relevant information can weRead more
Como posso fazer para o interpreter entender o que é o valor anterior de uma função matemática, como por exemplo: “Xn = 3,7(xn-1)” onde “n-1” significa o resultado da operação anterior do loop. Meio difícil de entender mas isso é nada menos que uma sequencia e serie matemática, mas queria aplicar ao python para resolverRead more
High quality 300kg/800lbs lifting magent/permanent magnetic lifter Feature and Application: Powerful Manual 1000kg/2500lbs permanent magnetic lifter has a magetic system formed by NdFeb magnetic materials with strong magnetism. It can control magnetic switch by rotating the handle. Details: Powerful Manual 1000kg/2500lbs permanent magnetic lifter has the characteristics of using no electricity, small volume, lightRead more
The sum of the sixth power sine series sin^6 1 o + sin^6 2 o + sin^6 3 o + …+ sin^6 89 o = m/n ( one degree) (eighty nine degrees) Find the values of m and nRead more
I think that I discovered another (c.f. Series expansion of expressions with Log and PolyLog functions) issue related to Series and PolyLog. Consider the following expression exp = (-16*Pi^2*Log[1 + Sqrt[x]])/3 + (16*Pi^2*Log[1 + Sqrt[x]])/ x^4 + (16*Pi^2*Log[1 + Sqrt[x]])/(3*x^2) + (32*Pi^2* Log[1 + Sqrt[x]])/(3*x) + (32*Pi^2*x*Log[1 + Sqrt[x]])/ 3 – (16*Log[1 + Sqrt[x]]^3)/3 +Read more
I am considering the order of magnitude of $ l_a(s)$ when $ s\to\infty$ : In[1]:= $ Assumptions = a > 0; Out[1]= l = 1/2 a (-2 Cos[a s] CosIntegral[a s] + Sin[a s] (\[Pi] – 2 SinIntegral[a s])); In[2]:= Limit[l, s -> \[Infinity]] Out[2]= 0 In[3]:= Series[l, {s, \[Infinity], 8}] // FullSimplify Out[3]= (*Read more
It is known that the power series $ \sum_{n=0}^\infty a_n x^n$ and $ \sum_{n=0}^\infty n a_n x^{n-1}$ have the same radius of convergence $ r$ . Is it true that if $ r<\infty$ and $ \sum_{n=0}^\infty na_n r^{n-1}$ converges then $ \sum_{n=0}^\infty a_n r^n$ converges, too? The same question for $ -r$ . If not,Read more
If $ F:V\to W$ is a smooth at $ a\in V$ function between finite-dimensional vector spaces over $ \mathbb{R}$ , then we have $ $ F(x) = \sum_{k=0}^N\frac{1}{k!}(D^kF)(a)[(x-a)^{\otimes k}]+\text{remainder}, $ $ where $ (D^kF)(a):\mathrm{Sym}^k(V)\to W$ are $ \mathbb{R}$ -linear maps. Algebraically, this is a statement about writing tuples of homogeneous polynomials of same degree asRead more