Search Results for ""

In the algebraic geometry of Grothendieck, a stack refers to a sheaf of categories. In particular, a stack is a presheaf of categories in which the following descent ...

The Andrews-Schur identity states sum_(k=0)^nq^(k^2+ak)[2n-k+a; k]_q =sum_(k=-infty)^inftyq^(10k^2+(4a-1)k)[2n+2a+2; n-5k]_q([10k+2a+2]_q)/([2n+2a+2]_q) (1) where [n; m]_q is ...

The word argument is used in several differing contexts in mathematics. The most common usage refers to the argument of a function, but is also commonly used to refer to the ...

Let P(x) be defined as the power series whose nth term has a coefficient equal to the nth prime p_n, P(x) = 1+sum_(k=1)^(infty)p_kx^k (1) = 1+2x+3x^2+5x^3+7x^4+11x^5+.... (2) ...

The backward difference is a finite difference defined by del _p=del f_p=f_p-f_(p-1). (1) Higher order differences are obtained by repeated operations of the backward ...

The Bernoulli inequality states (1+x)^n>1+nx, (1) where x>-1!=0 is a real number and n>1 an integer. This inequality can be proven by taking a Maclaurin series of (1+x)^n, ...

11 21 3 41 4 7 81 5 11 15 161 6 16 26 31 32 (1) The number triangle illustrated above (OEIS A008949) composed of the partial sums of binomial coefficients, a_(nk) = ...

If f(x) is piecewise continuous and has a generalized Fourier series sum_(i)a_iphi_i(x) (1) with weighting function w(x), it must be true that ...

A variable with a beta binomial distribution is distributed as a binomial distribution with parameter p, where p is distribution with a beta distribution with parameters ...

A binary bracketing is a bracketing built up entirely of binary operations. The number of binary bracketings of n letters (Catalan's problem) are given by the Catalan numbers ...