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The number of bases in which 1/p is a repeating decimal (actually, repeating b-ary) of length l is the same as the number of fractions 0/(p-1), 1/(p-1), ..., (p-2)/(p-1) ...

A harmonic number is a number of the form H_n=sum_(k=1)^n1/k (1) arising from truncation of the harmonic series. A harmonic number can be expressed analytically as ...

The partial differential equation u_(xy)+(N(u_x+u_y))/(x+y)=0.

The Rayleigh functions sigma_n(nu) for n=1, 2, ..., are defined as sigma_n(nu)=sum_(k=1)^inftyj_(nu,k)^(-2n), where +/-j_(nu,k) are the zeros of the Bessel function of the ...

Riddell's formula for unlabeled graphs is the Euler transform relating the number of unlabeled connected graphs on n nodes satisfying some property with the corresponding ...

Numerical differentiation is the process of finding the numerical value of a derivative of a given function at a given point. In general, numerical differentiation is more ...

The system of partial differential equations describing fluid flow in the absence of viscosity, given by (partialu)/(partialt)+u·del u=-(del P)/rho, where u is the fluid ...

Let f(x,y) be a homogeneous function of order n so that f(tx,ty)=t^nf(x,y). (1) Then define x^'=xt and y^'=yt. Then nt^(n-1)f(x,y) = ...

A number D that possesses no common divisor with a prime number p is either a quadratic residue or nonresidue of p, depending whether D^((p-1)/2) is congruent mod p to +/-1.

Gregory's formula is a formula that allows a definite integral of a function to be expressed by its sum and differences, or its sum by its integral and difference (Jordan ...