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At rational arguments p/q, the digamma function psi_0(p/q) is given by psi_0(p/q)=-gamma-ln(2q)-1/2picot(p/qpi) +2sum_(k=1)^([q/2]-1)cos((2pipk)/q)ln[sin((pik)/q)] (1) for ...

For a bivariate normal distribution, the distribution of correlation coefficients is given by P(r) = (1) = (2) = (3) where rho is the population correlation coefficient, ...

An elliptic partial differential equation given by del ^2psi+k^2psi=0, (1) where psi is a scalar function and del ^2 is the scalar Laplacian, or del ^2F+k^2F=0, (2) where F ...

Let z be defined as a function of w in terms of a parameter alpha by z=w+alphaphi(z). (1) Then Lagrange's inversion theorem, also called a Lagrange expansion, states that any ...

A sieving procedure that can be used in conjunction with Dixon's factorization method to factor large numbers n. Pick values of r given by r=|_sqrt(n)_|+k, (1) where k=1, 2, ...

A modified set of Chebyshev polynomials defined by a slightly different generating function. They arise in the development of four-dimensional spherical harmonics in angular ...

Laguerre-Gauss quadrature, also called Gauss-Laguerre quadrature or Laguerre quadrature, is a Gaussian quadrature over the interval [0,infty) with weighting function ...

Let T_n(x) be an arbitrary trigonometric polynomial T_n(x)=1/2a_0+{sum_(k=1)^n[a_kcos(kx)+b_ksin(kx)]} (1) with real coefficients, let f be a function that is integrable over ...

Gram's law (Hutchinson 1925; Edwards 2001, pp. 125, 127, and 171) is the tendency for zeros of the Riemann-Siegel function Z(t) to alternate with Gram points. Stated more ...

The word "harmonic" has several distinct meanings in mathematics, none of which is obviously related to the others. Simple harmonic motion or "harmonic oscillation" refers to ...