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The expansion of the two sides of a sum equality in terms of polynomials in x^m and y^k, followed by closed form summation in terms of x and y. For an example of the ...

Let a and b be nonzero integers such that a^mb^n!=1 (except when m=n=0). Also let T(a,b) be the set of primes p for which p|(a^k-b) for some nonnegative integer k. Then ...

Doob (1996) defines a stochastic process as a family of random variables {x(t,-),t in J} from some probability space (S,S,P) into a state space (S^',S^'). Here, J is the ...

If P(n) is a sentential formula depending on a variable n ranging in a set of real numbers, the sentence P(n) for every sufficiently large n (1) means exists N such that P(n) ...

For a curve with radius vector r(t), the unit tangent vector T^^(t) is defined by T^^(t) = (r^.)/(|r^.|) (1) = (r^.)/(s^.) (2) = (dr)/(ds), (3) where t is a parameterization ...

In logic, a term is a variable, constant, or the result of acting on variables and constants by function symbols. In algebra, a term is a product of the form x^n (in the ...

The tilde is the mark "~" placed on top of a symbol to indicate some special property. x^~ is voiced "x-tilde." The tilde symbol is commonly used to denote an operator. In ...

There are at least two meanings of the term "total derivative" in mathematics. The first is as an alternate term for the convective derivative. The total derivative is the ...

Let x and y be vectors. Then the triangle inequality is given by |x|-|y|<=|x+y|<=|x|+|y|. (1) Equivalently, for complex numbers z_1 and z_2, ...

A triply periodic function is a function having three distinct periods. Jacobi (1835) proved that a single-valued univariate function cannot have more than two distinct ...