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The scalar form of Laplace's equation is the partial differential equation del ^2psi=0, (1) where del ^2 is the Laplacian. Note that the operator del ^2 is commonly written ...

The Riemann zeta function is an extremely important special function of mathematics and physics that arises in definite integration and is intimately related with very deep ...

A function f in C^infty(R^n) is called a Schwartz function if it goes to zero as |x|->infty faster than any inverse power of x, as do all its derivatives. That is, a function ...

An arithmetic progression, also known as an arithmetic sequence, is a sequence of n numbers {a_0+kd}_(k=0)^(n-1) such that the differences between successive terms is a ...

The Cauchy product of two sequences f(n) and g(n) defined for nonnegative integers n is defined by (f degreesg)(n)=sum_(k=0)^nf(k)g(n-k).

Given a series of the form A(z)=sum_(k)a_kz^k, the notation [z^k](A(z)) is used to indicate the coefficient a_k (Sedgewick and Flajolet 1996). This corresponds to the Wolfram ...

Given an arithmetic series {a_1,a_1+d,a_1+2d,...}, the number d is called the common difference associated to the sequence.

The term faltung is variously used to mean convolution and a function of bilinear forms. Let A and B be bilinear forms A = A(x,y)=sumsuma_(ij)x_iy_i (1) B = ...

Taylor's inequality is an estimate result for the value of the remainder term R_n(x) in any n-term finite Taylor series approximation. Indeed, if f is any function which ...

A phenomenological law also called the first digit law, first digit phenomenon, or leading digit phenomenon. Benford's law states that in listings, tables of statistics, ...