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A polynomial sequence p_n(x) is called the basic polynomial sequence for a delta operator Q if 1. p_0(x)=1, 2. p_n(0)=0 for all n>0, 3. Qp_n(x)=np_(n-1)(x). If p_n(x) is a ...
Multiple series generalizations of basic hypergeometric series over the unitary groups U(n+1). The fundamental theorem of U(n) series takes c_1, ..., c_n and x_1, ..., x_n as ...
An operator T which maps some basic polynomial sequence p_n(x) into another basic polynomial sequence q_n(x).
One of the basic objects treated in a given formal language system. The term is sometimes also used as a synonym for urelement.
If the property of being an object is expressed by a basic predicate of the system, then such a predicate (if it exists) is called a universal predicate, or universal ...
An abstract algebra concerned with results valid for many different kinds of spaces. Modules are the basic tools used in homological algebra.
A shift-invariant operator Q for which Qx is a nonzero constant. 1. Qa=0 for every constant a. 2. If p(x) is a polynomial of degree n, Qp(x) is a polynomial of degree n-1. 3. ...
The straightedge and the compass. The name is due to the fact that connecting points with segments, prolonging segments and drawing circles with a given center and a given ...
A statement, also known as an axiom, which is taken to be true without proof. Postulates are the basic structure from which lemmas and theorems are derived. The whole of ...
A Lie algebra g is solvable when its Lie algebra commutator series, or derived series, g^k vanishes for some k. Any nilpotent Lie algebra is solvable. The basic example is ...
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