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A generalization of the p-adic norm first proposed by Kürschák in 1913. A valuation |·| on a field K is a function from K to the real numbers R such that the following ...

For a single variate X having a distribution P(x) with known population mean mu, the population variance var(X), commonly also written sigma^2, is defined as ...

Let c_k be the number of vertex covers of a graph G of size k. Then the vertex cover polynomial Psi_G(x) is defined by Psi_G(x)=sum_(k=0)^(|G|)c_kx^k, (1) where |G| is the ...

The Wallis formula follows from the infinite product representation of the sine sinx=xproduct_(n=1)^infty(1-(x^2)/(pi^2n^2)). (1) Taking x=pi/2 gives ...

The Walsh functions consist of trains of square pulses (with the allowed states being -1 and 1) such that transitions may only occur at fixed intervals of a unit time step, ...

Although Bessel functions of the second kind are sometimes called Weber functions, Abramowitz and Stegun (1972) define a separate Weber function as ...

An algorithm which finds a polynomial recurrence for terminating hypergeometric identities of the form sum_(k)(n; ...

The abc conjecture is a conjecture due to Oesterlé and Masser in 1985. It states that, for any infinitesimal epsilon>0, there exists a constant C_epsilon such that for any ...

Number Theory

There are a great many beautiful identities involving q-series, some of which follow directly by taking the q-analog of standard combinatorial identities, e.g., the ...