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There are several statistical quantities called means, e.g., harmonic mean, geometric mean, arithmetic-geometric mean, and root-mean-square. When applied to two elements a ...

There are a number of functions in various branches of mathematics known as Riemann functions. Examples include the Riemann P-series, Riemann-Siegel functions, Riemann theta ...

A technical mathematical object defined in terms of a polynomial ring of n variables over a field k. Syzygies occur in tensors at rank 5, 7, 8, and all higher ranks, and play ...

T-integration, which stands for "tunable numerical integration," is a fast, accurate, and numerically stable numerical integration formula given by ...

Bertelsen's number is an erroneous name erroneously given to the erroneous value of pi(10^9)=50847478, where pi(x) is the prime counting function. This value is 56 lower than ...

Let B_t={B_t(omega)/omega in Omega}, t>=0, be one-dimensional Brownian motion. Integration with respect to B_t was defined by Itô (1951). A basic result of the theory is that ...

A method for finding recurrence relations for hypergeometric polynomials directly from the series expansions of the polynomials. The method is effective and easily ...

A transcendental number is a (possibly complex) number that is not the root of any integer polynomial, meaning that it is not an algebraic number of any degree. Every real ...

The integral transform defined by (Kphi)(x)=int_0^infty(x^2-t^2)_+^(lambda/2)P_nu^lambda(t/x)phi(t)dt, where y_+^alpha is the truncated power function and P_nu^lambda(x) is ...

Since the derivative of a constant is zero, any constant may be added to an indefinite integral (i.e., antiderivative) and will still correspond to the same integral. Another ...