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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 ...

Watson (1939) considered the following three triple integrals, I_1 = 1/(pi^3)int_0^piint_0^piint_0^pi(dudvdw)/(1-cosucosvcosw) (1) = (4[K(1/2sqrt(2))]^2)/(pi^2) (2) = ...

The "Cartesian ovals," sometimes also known as the Cartesian curve or oval of Descartes, are the quartic curve consisting of two ovals. They were first studied by Descartes ...

Let P(z) and Q(z) be univariate polynomials in a complex variable z, and let the polynomial degrees of P and Q satisfy deg(Q)>=deg(P+2). Then int_gamma(P(z))/(Q(z))dz = ...

Cubic lattice sums include the following: b_2(2s) = sum^'_(i,j=-infty)^infty((-1)^(i+j))/((i^2+j^2)^s) (1) b_3(2s) = ...

The product C of two matrices A and B is defined as c_(ik)=a_(ij)b_(jk), (1) where j is summed over for all possible values of i and k and the notation above uses the ...

The reversal of a positive integer abc...z is z...cba. The reversal of a positive integer n is implemented in the Wolfram Language as IntegerReverse[n]. A positive integer ...

"Stampacchia's theorem" is a name given to any number of related results in functional analysis, and while the body of the theorem often varies depending on the literature ...

A run is a sequence of more than one consecutive identical outcomes, also known as a clump. Let R_p(r,n) be the probability that a run of r or more consecutive heads appears ...

An Andreini tessellation is a three-dimensional equivalent of a semiregular tessellation. There are 28 such tessellations.