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A universal sentence is a sentence (i.e., formula of the predicate calculus without free variables) whose variables are universally quantified.

A set of three conjectures proposed by Weil in 1942 for extending Riemann hypothesis-like statements to classes of mathematical structures. The conjectures were proved by ...

Every nonempty set of positive integers contains a smallest member.

The probability law on the space of continuous functions g with g(0)=0, induced by the Wiener process.

The anti-self-dual Yang-Mills equation is the system of partial differential equations ...

sum_(y=0)^m(-1)^(m-y)q^((m-y; 2))[m; y]_q(1-wq^m)/(q-wq^y) ×(1-wq^y)^m(-(1-z)/(1-wq^y);q)_y=(1-z)^mq^((m; 2)), where [n; y]_q is a q-binomial coefficient.

Comprehensive encyclopedia of mathematics with 13,000 detailed entries. Continually updated, extensively illustrated, and with interactive examples.

There are two kinds of Bell polynomials. A Bell polynomial B_n(x), also called an exponential polynomial and denoted phi_n(x) (Bell 1934, Roman 1984, pp. 63-67) is a ...

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 special case of Hölder's sum inequality with p=q=2, (sum_(k=1)^na_kb_k)^2<=(sum_(k=1)^na_k^2)(sum_(k=1)^nb_k^2), (1) where equality holds for a_k=cb_k. The inequality is ...