Has anyone tried to make a connection between the Mandelbrot set and the non-trivial zeros the zeta function?
Looking at the Mandelbrot set, it appears that all points are to the left of the line 0.5 + t*I, and to the right of the point -2. So the set is bounded on the left by the trivial zeros...3
In mathematics, particularly linear algebra and numerical analysis, the Gram–Schmidt process is a method for orthonormalising a set of vectors in an inner product space, most commonly the Euclidean space Rn equipped with the standard inner product. The Gram–Schmidt process takes a finite, linearly independent set S = {v1, ..., vk} for k ≤ n and generates an orthogonal set S′ = {u1, ..., uk} that spans the same k-dimensional subspace of Rn as S.
The method is named after Jørgen Pedersen Gram and Erhard Schmidt, but Pierre-Simon Laplace had been familiar with it before Gram and Schmidt. In the theory...
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In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by LCM(a, b), is the smallest positive integer that is divisible by both a and b. Since division of integers by zero is undefined, this definition has meaning only if a and b are both different from zero. However, some authors define lcm(a,0) as 0 for all a, which is the result of taking the lcm to be the least upper bound in the lattice of divisibility.
The LCM is the "lowest common denominator" (LCD) that can be used before fractions can be added...
In mathematics, the affinely extended real number system is obtained from the real number system ℝ by adding two elements: + ∞ and – ∞ (read as positive infinity and negative infinity respectively). These new elements are not real numbers. It is useful in describing various limiting behaviors in calculus and mathematical analysis, especially in the theory of measure and integration. The affinely extended real number system is denoted
R
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{\displaystyle {\overline {\mathbb...
I'm struggling with the following calculus question.
Let there be two functions $f,g : [a, \infty) \to \mathbb R$ such that:
$g$ is monotonic, differentiable and has a limit at zero
$f$ is continues such that $\int_a^b (f) < M \in \mathbb R$.
Prove that integral $\int_a^{\infty} f(x) * g(x)$...
