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Solve $f(\lfloor x \rfloor)=\lfloor f(x) \rfloor$

I've been trying to solve the equation $f(\lfloor x \rfloor)=\lfloor f(x) \rfloor$ for real $x$ and polynomials $f$. Of course all integer polynomials work, but I have no proof of this being the only ...
1 vote
9 views

Find the maximum value of a linear system c = A*b (matrix multiplication)

Assuming there is a square matrix A and vector b about to be multiplied. [A]{b}={c} However I am interested only in the maximum value within the resulted vector c. Is there a way to find that without ...
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13 views

Convergence of the gauss hypergeometric function in 'Generalized hypergeometric functions', L.J. Slater

the Gauss hypergeometric function is defined by: $$\label{e:pFq} {}_{2}F_1(a;b;z)=\sum_{n=0}^{\infty}\frac{(a)_n (b)_n}{(c)_n}\frac{z^n}{n!}=\sum_{n=0}^{\infty}u_n,$$ ...
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Angle Subtraction as a corollary to Angle Addition

I'm working with Greenberg's Euclidean and Non-Euclidean Geometries: Development and History 4th Edition. For a copy of the axioms used, see https://www.ms.uky.edu/~droyster/courses/fall11/ma341/...
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17 views

Defining surreal addition on signed ordinals

Consider surreal numbers as signed ordinals $\alpha\rightarrow\{-,+\}$. Suppose we already have $x<y$ defined for any two surreals, as well as $F|G$ as the simplest surreal $z$ strictly between the ...
• 2,980
22 views

Prove that Mobius map on the upper half plane is analytic.

Let $\mathbb{H}^2 = \{x \in \mathbb{C} \mid \Im (z) >0\}$ be the upper half plane. Then prove that $T: \mathbb{H}^2 \rightarrow \mathbb{H}^2$ defined by $T(z) = \displaystyle{\frac{az+b}{cz+d}}$ ...
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33 views

Finding directional angle of vector in $\mathbb{R}^2$

I'm not sure if this is correct or not and need someone to check. I have a vector $\vec{v} = 4\left(\frac{-1}{2}, 1\right) - \frac{1}{2}(4, 8)$ I simplified it to $(-4, 0)$ So the directional angle ...
65 views

14 views

Does a sequence of finite integrals with non-negative integrands which converges on a measure space also converge on any measurable set?

Let $(X, \mathcal{A}, \mu)$ denote a measure space, and let $\{f_n\}_{n=1}^{\infty}$ be a sequence of non-negative, real-valued functions on $X$ for which each integral in (1) is finite, and suppose ...
• 59
19 views

How to generalize the triangles condition in Morera's Theorem to translates and dilates of any toy contour?

I saw in COMPLEX ANALYSIS written by Stein the generalization of Morera's Theorem, but the hint made me confused. Why the fe(x) defined there satisfy the condition(16), namely that integral of fe(x) ...
1 vote
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