Search Results for ""

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 ...

Every irrational number x can be expanded in a unique continued fraction expansion x=b_0+(e_1)/(b_1+(e_2)/(b_2+(e_3)/(b_3+...)))=[b_0;e_1b_1,e_2b_2,e_3b_3,...] such that b_0 ...

Analytic continuation (sometimes called simply "continuation") provides a way of extending the domain over which a complex function is defined. The most common application is ...

Apéry's constant is defined by zeta(3)=1.2020569..., (1) (OEIS A002117) where zeta(z) is the Riemann zeta function. B. Haible and T. Papanikolaou computed zeta(3) to 1000000 ...

Let x be a real number, and let R be the set of positive real numbers mu for which 0<|x-p/q|<1/(q^mu) (1) has (at most) finitely many solutions p/q for p and q integers. Then ...

In this work, the name Pythagoras's constant will be given to the square root of 2, sqrt(2)=1.4142135623... (1) (OEIS A002193), which the Pythagoreans proved to be ...

Let z be defined as a function of w in terms of a parameter alpha by z=w+alphaphi(z). (1) Then Lagrange's inversion theorem, also called a Lagrange expansion, states that any ...

The permanent is an analog of a determinant where all the signs in the expansion by minors are taken as positive. The permanent of a matrix A is the coefficient of x_1...x_n ...

The Lambert W-function, also called the omega function, is the inverse function of f(W)=We^W. (1) The plot above shows the function along the real axis. The principal value ...

Unlike quadratic, cubic, and quartic polynomials, the general quintic cannot be solved algebraically in terms of a finite number of additions, subtractions, multiplications, ...