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If a function phi is harmonic in a sphere, then the value of phi at the center of the sphere is the arithmetic mean of its value on the surface.

A geometric sequence is a sequence {a_k}, k=0, 1, ..., such that each term is given by a multiple r of the previous one. Another equivalent definition is that a sequence is ...

The identity PVint_(-infty)^inftyF(phi(x))dx=PVint_(-infty)^inftyF(x)dx (1) holds for any integrable function F(x) and phi(x) of the form ...

(theta_3(z,t)theta_4(z,t))/(theta_4(2z,2t))=(theta_3(0,t)theta_4(0,t))/(theta_4(0,2t))=(theta_2(z,t)theta_1(z,t))/(theta_1(2z,2t)), where theta_i are Jacobi theta functions. ...

A multinomial series is generalization of the binomial series discovered by Johann Bernoulli and Leibniz. The multinomial series arises in a generalization of the binomial ...

The series which arises in the binomial theorem for negative integer -n, (x+a)^(-n) = sum_(k=0)^(infty)(-n; k)x^ka^(-n-k) (1) = sum_(k=0)^(infty)(-1)^k(n+k-1; k)x^ka^(-n-k) ...

A number theoretic function is a function whose domain is the set of positive integers.

The number of digits used to perform a given computation. The concepts of accuracy and precision are both closely related and often confused. While the accuracy of a number x ...

A metric space Z^^ in which the closure of a congruence class B(j,m) is the corresponding congruence class {x in Z^^|x=j (mod m)}.

A word derived from the Latin roots quad- (four) and via (ways, roads), therefore a crossing of four roads. In medieval universities, the quadrivium consisted of the four ...