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The study of an extension of derivatives and integrals to noninteger orders. Fractional calculus is based on the definition of the fractional integral as ...

A Fredholm integral equation of the first kind is an integral equation of the form f(x)=int_a^bK(x,t)phi(t)dt, (1) where K(x,t) is the kernel and phi(t) is an unknown ...

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 ...

Gauss's continued fraction is given by the continued fraction ...

If u_n>0 and given B(n) a bounded function of n as n->infty, express the ratio of successive terms as |(u_n)/(u_(n+1))|=1+h/n+(B(n))/(n^r) for r>1. The series converges for ...

A generalized Vandermonde matrix of two sequences a and b where a is an increasing sequence of positive integers and b is an increasing sequence of nonnegative integers of ...

The term "gradient" has several meanings in mathematics. The simplest is as a synonym for slope. The more general gradient, called simply "the" gradient in vector analysis, ...

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 ...

Let {a_n} be a nonnegative sequence and f(x) a nonnegative integrable function. Define A_n=sum_(k=1)^na_k (1) and F(x)=int_0^xf(t)dt (2) and take p>1. For sums, ...

Consider a first-order logic formula Phi in Skolemized form forall x_1... forall x_nS. Then the Herbrand universe H of S is defined by the following rules. 1. All constants ...