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Let B_t={B_t(omega)/omega in Omega}, t>=0, be one-dimensional Brownian motion. Integration with respect to B_t was defined by Itô (1951). A basic result of the theory is that ...

The asymptotic series for the gamma function is given by (1) (OEIS A001163 and A001164). The coefficient a_n of z^(-n) can given explicitly by ...

The Lucas numbers are the sequence of integers {L_n}_(n=1)^infty defined by the linear recurrence equation L_n=L_(n-1)+L_(n-2) (1) with L_1=1 and L_2=3. The nth Lucas number ...

A formula of first-order logic is in prenex normal form if it is of the form Q_1x_1...Q_nx_nM, (1) where each Q_i is a quantifier forall ("for all") or exists ("exists") and ...

An operator definition of a function. A Rodrigues formula may be converted into a Schläfli integral.

A formula is called satisfiable if it takes at least one true value in some interpretation.

A formula whose truth table contains only false in any interpretation is called unsatisfiable.

The Wallis formula follows from the infinite product representation of the sine sinx=xproduct_(n=1)^infty(1-(x^2)/(pi^2n^2)). (1) Taking x=pi/2 gives ...

Deciding whether a given Boolean formula in conjunctive normal form has an assignment that makes the formula "true." In 1971, Cook showed that the problem is NP-complete.

A formula for numerical integration, (1) where C_(2n) = sum_(i=0)^(n)f_(2i)cos(tx_(2i))-1/2[f_(2n)cos(tx_(2n))+f_0cos(tx_0)] (2) C_(2n-1) = ...