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The number of multisets of length k on n symbols is sometimes termed "n multichoose k," denoted ((n; k)) by analogy with the binomial coefficient (n; k). n multichoose k is ...

An occurrence of a variable in a logic formula which is not inside the scope of a quantifier.

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

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 ...

Roman (1984, p. 26) defines "the" binomial identity as the equation p_n(x+y)=sum_(k=0)^n(n; k)p_k(y)p_(n-k)(x). (1) Iff the sequence p_n(x) satisfies this identity for all y ...

A sentence is a logic formula in which every variable is quantified. The concept of a sentence is important because formulas with variables that are not quantified are ...

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 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.

Roman (1984, p. 2) describes umbral calculus as the study of the class of Sheffer sequences. Umbral calculus provides a formalism for the systematic derivation and ...