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Planck's's radiation function is the function f(x)=(15)/(pi^4)1/(x^5(e^(1/x)-1)), (1) which is normalized so that int_0^inftyf(x)dx=1. (2) However, the function is sometimes ...

Pythagoras's theorem states that the diagonal d of a square with sides of integral length s cannot be rational. Assume d/s is rational and equal to p/q where p and q are ...

The direct product of the rings R_gamma, for gamma some index set I, is the set product_(gamma in I)R_gamma={f:I-> union _(gamma in I)R_gamma|f(gamma) in R_gamma all gamma in ...

The Rogers-Ramanujan continued fraction is a generalized continued fraction defined by R(q)=(q^(1/5))/(1+q/(1+(q^2)/(1+(q^3)/(1+...)))) (1) (Rogers 1894, Ramanujan 1957, ...

The extension field K of a field F is called a splitting field for the polynomial f(x) in F[x] if f(x) factors completely into linear factors in K[x] and f(x) does not factor ...

The successive overrelaxation method (SOR) is a method of solving a linear system of equations Ax=b derived by extrapolating the Gauss-Seidel method. This extrapolation takes ...

The word weight has many uses in mathematics. It can refer to a function w(x) (also called a weighting function or weighting function) used to normalize orthogonal functions. ...

A colossally abundant number is a positive integer n for which there is a positive exponent epsilon such that (sigma(n))/(n^(1+epsilon))>=(sigma(k))/(k^(1+epsilon)) for all ...

A module is a mathematical object in which things can be added together commutatively by multiplying coefficients and in which most of the rules of manipulating vectors hold. ...

A polynomial factorization algorithm that proceeds by considering the vector of coefficients of a polynomial P, calculating b_i=P(i)/a_i, constructing the Lagrange ...