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Given a series of positive terms u_i and a sequence of finite positive constants a_i, let rho=lim_(n->infty)(a_n(u_n)/(u_(n+1))-a_(n+1)). 1. If rho>0, the series converges. ...

A convergence test also called "de Morgan's and Bertrand's test." If the ratio of terms of a series {a_n}_(n=1)^infty can be written in the form ...

The exponential sum function e_n(x), sometimes also denoted exp_n(x), is defined by e_n(x) = sum_(k=0)^(n)(x^k)/(k!) (1) = (e^xGamma(n+1,x))/(Gamma(n+1)), (2) where ...

Multisection of a mathematical quantity or figure is division of it into a number of (usually) equal parts. Division of a quantity into two equal parts is known as bisection, ...

A generalized hypergeometric function _pF_q[alpha_1,alpha_2,...,alpha_p; beta_1,beta_2,...,beta_q;z], is said to be Saalschützian if it is k-balanced with k=1, ...

The asymptotic series of the Airy function Ai(z) (and other similar functions) has a different form in different sectors of the complex plane.

Generally speaking, a Green's function is an integral kernel that can be used to solve differential equations from a large number of families including simpler examples such ...

The Mittag-Leffler function (Mittag-Leffler 1903, 1905) is an entire function defined by the series E_alpha(z)=sum_(k=0)^infty(z^k)/(Gamma(alphak+1)) (1) for alpha>0. It is ...

The Euclidean algorithm, also called Euclid's algorithm, is an algorithm for finding the greatest common divisor of two numbers a and b. The algorithm can also be defined for ...

An ordinary differential equation (frequently called an "ODE," "diff eq," or "diffy Q") is an equality involving a function and its derivatives. An ODE of order n is an ...