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A metric space is a set S with a global distance function (the metric g) that, for every two points x,y in S, gives the distance between them as a nonnegative real number ...

A product involving an infinite number of terms. Such products can converge. In fact, for positive a_n, the product product_(n=1)^(infty)a_n converges to a nonzero number iff ...

According to Pólya, the Cartesian pattern is the resolution method for arithmetical or geometrical problems based on equations. The first step is to translate the question ...

A number x is said to have "n figures" if it takes n digits to express it. The number of figures is therefore equal to one more than the power of 10 in the scientific ...

A branch point of an analytic function is a point in the complex plane whose complex argument can be mapped from a single point in the domain to multiple points in the range. ...

A transformation of a hypergeometric function,

where _8phi_7 is a q-hypergeometric function.

_2phi_1(a,q^(-n);c;q,q)=(a^n(c/a,q)_n)/((a;q)_n), where _2phi_1(a,b;c;q,z) is a q-hypergeometric function.

Given a system of ordinary differential equations of the form d/(dt)[x; y; v_x; v_y]=-[0 0 -1 0; 0 0 0 -1; Phi_(xx)(t) Phi_(yx)(t) 0 0; Phi_(xy)(t) Phi_(yy)(t) 0 0][x; y; ...

Given a triangle DeltaABC, construct the contact triangle DeltaT_AT_BT_C. Now extend lines parallel to the sides of the contact triangle from the Gergonne point. These ...