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A sequence s_n(x) is called a Sheffer sequence iff its generating function has the form sum_(k=0)^infty(s_k(x))/(k!)t^k=A(t)e^(xB(t)), (1) where A(t) = A_0+A_1t+A_2t^2+... ...

The algebraic connectivity of a graph is the numerically second smallest eigenvalue (counting multiple eigenvalues separately) of the Laplacian matrix of a graph G. In other ...

A method for numerical solution of a second-order ordinary differential equation y^('')=f(x,y) first expounded by Gauss. It proceeds by introducing a function delta^(-2)f ...

If we expand the determinant of a matrix A using determinant expansion by minors, first in terms of the minors of order r formed from any r rows, with their complementaries, ...

Debye's asymptotic representation is an asymptotic expansion for a Hankel function of the first kind with nu approx x. For 1-nu/x>epsilon, nu/x=sinalpha, ...

The variable phi (also denoted am(u,k)) used in elliptic functions and elliptic integrals is called the amplitude (or Jacobi amplitude). It can be defined by phi = am(u,k) ...

The bei_nu(z) function is defined through the equation J_nu(ze^(3pii/4))=ber_nu(z)+ibei_nu(z), (1) where J_nu(z) is a Bessel function of the first kind, so ...

The function ber_nu(z) is defined through the equation J_nu(ze^(3pii/4))=ber_nu(z)+ibei_nu(z), (1) where J_nu(z) is a Bessel function of the first kind, so ...

A second-order ordinary differential equation arising in the study of stellar interiors, also called the polytropic differential equations. It is given by ...

The Laplace transform is an integral transform perhaps second only to the Fourier transform in its utility in solving physical problems. The Laplace transform is particularly ...