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Alpha is the name for the first letter in the Greek alphabet: alpha. In finance, alpha is a financial measure giving the difference between a fund's actual return and its ...

The bend of a circle C mutually tangent to three other circles is defined as the signed curvature of C. If the contacts are all external, the signs of the bends of all four ...

The determinant of a binary quadratic form Au^2+2Buv+Cv^2 is defined as D=AC-B^2. It is equal to 1/4 of the corresponding binary quadratic form discriminant. Unfortunately, ...

The discriminant of a binary quadratic form au^2+buv+cv^2 is defined by d=4ac-b^2. It is equal to four times the corresponding binary quadratic form determinant. ...

Let where (alpha)_j is a Pochhammer symbol, and let alpha be a negative integer. Then S(alpha,beta,m;z)=(Gamma(beta+1-m))/(Gamma(alpha+beta+1-m)), where Gamma(z) is the gamma ...

B(x,y)=[x y; +/-ty +/-x]. (1) It satisfies B(x_1,y_1)B(x_2,y_2)=B(x_1x_2+/-ty_1y_2,x_1y_2+/-y_1x_2). (2) Powers of the matrix are defined by B^n = [x y; ty x]^n (3) = [x_n ...

The absence of contradiction (i.e., the ability to prove that a statement and its negative are both true) in an Axiomatic system is known as consistency.

The radial curve of the deltoid x = 1/3a[2cost+cos(2t)] (1) y = 1/3a[2sint-sin(2t)] (2) with pedal point (x_0,y_0) is x_p = 1/6[3x+cost+3xcost-cos(2t)-3ysint] (3) y_p = ...

A piecewise regular function that 1. Has a finite number of finite discontinuities and 2. Has a finite number of extrema can be expanded in a Fourier series which converges ...

Expanded notation is the term given in elementary mathematics education for the expansion of a positive integer in the form sum_(k)b_k10^k, i.e., as a sum of appropriate ...