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An indicial equation, also called a characteristic equation, is a recurrence equation obtained during application of the Frobenius method of solving a second-order ordinary ...

The inverse haversine function hav^(-1)(z) is defined by hav^(-1)(z)=2sin^(-1)(sqrt(z)). (1) The inverse haversine is implemented in the Wolfram Language as ...

The spherical harmonics form a complete orthogonal system, so an arbitrary real function f(theta,phi) can be expanded in terms of complex spherical harmonics by ...

Let A be an involutive algebra over the field C of complex numbers with involution xi|->xi^♯. Then A is a left Hilbert algebra if A has an inner product <·,·> satisfying: 1. ...

Line segment picking is the process of picking line segments at random within a given shape in the plane, in space, or in a higher dimension. The most natural definition of a ...

The Littlewood conjecture states that for any two real numbers x,y in R, lim inf_(n->infty)n|nx-nint(nx)||ny-nint(ny)|=0 where nint(z) denotes the nearest integer function. ...

The study of number fields by embedding them in a local field is called local class field theory. Information about an equation in a local field may give information about ...

A method for computing the prime counting function. Define the function T_k(x,a)=(-1)^(beta_0+beta_1+...+beta_(a-1))|_x/(p_1^(beta_0)p_2^(beta_1)...p_a^(beta_(a-1)))_|, (1) ...

A figurate number corresponding to a pentagonal pyramid. The first few are 1, 6, 18, 40, 75, ... (OEIS A002411). The generating function for the pentagonal pyramidal numbers ...

An n-persistent number is a positive integer k which contains the digits 0, 1, ..., 9 (i.e., is a pandigital number), and for which 2k, ..., nk also share this property. No ...