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Let Xi be the xi-function defined by Xi(iz)=1/2(z^2-1/4)pi^(-z/2-1/4)Gamma(1/2z+1/4)zeta(z+1/2). (1) Xi(z/2)/8 can be viewed as the Fourier transform of the signal ...
De Grey (2018) found the first examples of unit-distance graphs with chromatic number 5, thus demonstrating that the solution to the Hadwiger-Nelson problem (i.e., the ...
The asymptotic form of the n-step Bernoulli distribution with parameters p and q=1-p is given by P_n(k) = (n; k)p^kq^(n-k) (1) ∼ 1/(sqrt(2pinpq))e^(-(k-np)^2/(2npq)) (2) ...
An e-prime is a prime number appearing in the decimal expansion of e. The first few are 2, 271, 2718281, ...
The constant e with decimal expansion e=2.718281828459045235360287471352662497757... (OEIS A001113) can be computed to 10^9 digits of precision in 10 CPU-minutes on modern ...
A graph G on more than two vertices is said to be k-connected (or k-vertex connected, or k-point connected) if there does not exist a vertex cut of size k-1 whose removal ...
One form of van der Waerden's theorem states that for all positive integers k and r, there exists a constant n(r,k) such that if n_0>=n(r,k) and {1,2,...,n_0} subset C_1 ...
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