Search Results for ""

An algorithm which finds rational function extrapolations of the form R_(i(i+1)...(i+m))=(P_mu(x))/(P_nu(x))=(p_0+p_1x+...+p_mux^mu)/(q_0+q_1x+...+q_nux^nu) and can be used ...

Gives a matrix representation b_i of a braid group in terms of (n-1)×(n-1) matrices. A -t always appears in the (i,i) position. b_1 = [-t 0 0 ... 0; -1 1 0 ... 0; 0 0 1 ... ...

The only known classically known algebraic curve of curve genus g>1 that has an explicit parametrization (x(t),y(t)) in terms of standard special functions (Burnside 1893, ...

Let S be a collection of subsets of a set X, mu:S->[0,infty] a set function, and mu^* the outer measure induced by mu. The measure mu^_ that is the restriction of mu^* to the ...

Assume that f is a nonnegative real function on [0,infty) and that the two integrals int_0^inftyx^(p-1-lambda)[f(x)]^pdx (1) int_0^inftyx^(q-1+mu)[f(x)]^qdx (2) exist and are ...

For F_n the nth Fibonacci number, F_(n-1)F_(n+1)-F_n^2=(-1)^n. This identity was also discovered by Simson (Coxeter and Greitzer 1967, p. 41; Coxeter 1969, pp. 165-168; Wells ...

Approximations to Catalan's constant include K approx (9/(10))^(5/6) (1) approx ln(ln892)-1 (2) approx (1/(96))^(1/52) (3) approx (4/(51))^(1/29) (4) approx ...

Catalan's triangle is the number triangle 1 ; 1 1 ; 1 2 2 ; 1 3 5 5 ; 1 4 9 14 14 ; 1 5 14 28 42 42 ; 1 6 20 48 90 132 132 (1) (OEIS A009766) with entries given by ...

A game in which no draw is possible. Steinhaus (1999, p. 16) stated that all categorical games are unfair, but this is incorrect. For example, the game "Odds or Evens" pits ...

A multiway system that generates causal networks which are all isomorphic as acyclic digraphs is said to exhibit causal invariance, and the causal network itself is also said ...