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A modified spherical Bessel function of the first kind (Abramowitz and Stegun 1972), also called a "spherical modified Bessel function of the first kind" (Arfken 1985), is ...

A modified spherical Bessel function of the second kind, also called a "spherical modified Bessel function of the first kind" (Arfken 1985) or (regrettably) a "modified ...

A procedure for determining the behavior of an nth order ordinary differential equation at a removable singularity without actually solving the equation. Consider ...

The Jacobi polynomials, also known as hypergeometric polynomials, occur in the study of rotation groups and in the solution to the equations of motion of the symmetric top. ...

Apéry's numbers are defined by A_n = sum_(k=0)^(n)(n; k)^2(n+k; k)^2 (1) = sum_(k=0)^(n)([(n+k)!]^2)/((k!)^4[(n-k)!]^2) (2) = _4F_3(-n,-n,n+1,n+1;1,1,1;1), (3) where (n; k) ...

A determinant used to determine in which coordinate systems the Helmholtz differential equation is separable (Morse and Feshbach 1953). A determinant S=|Phi_(mn)|=|Phi_(11) ...

Gaussian elimination is a method for solving matrix equations of the form Ax=b. (1) To perform Gaussian elimination starting with the system of equations [a_(11) a_(12) ... ...

Matrix diagonalization is the process of taking a square matrix and converting it into a special type of matrix--a so-called diagonal matrix--that shares the same fundamental ...

Given a regular surface M, an asymptotic curve is formally defined as a curve x(t) on M such that the normal curvature is 0 in the direction x^'(t) for all t in the domain of ...

The first solution to Lamé's differential equation, denoted E_n^m(x) for m=1, ..., 2n+1. They are also called Lamé functions. The product of two ellipsoidal harmonics of the ...