|
Pincherle Polynomials
In mathematics, the Pincherle polynomials P''n''(''x'') are polynomials introduced by given by the generating function :\displaystyle (1-3xt+t^3)^=\sum^\infty _P_n(x)t^n Humbert polynomials In mathematics, the Humbert polynomials π(''x'') are a generalization of Pincherle polynomials introduced by given by the generating function :\displaystyle (1-mxt+t^m)^=\sum^\infty _\pi^\lambda_(x)t^n . See also *Umbral calculus In mathem ... are a generalization of Pincherle polynomials References * * Polynomials {{polynomial-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polynomials
In mathematics, a polynomial is an expression (mathematics), expression consisting of indeterminate (variable), indeterminates (also called variable (mathematics), variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An example of a polynomial of a single indeterminate is . An example with three indeterminates is . Polynomials appear in many areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problem (mathematics education), word problems to complicated scientific problems; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; they are used in calculus and numerical analysis to approximate other functions. In advanced mathematics, polynomials are used to construct polynomial rings and algebraic variety ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generating Function
In mathematics, a generating function is a way of encoding an infinite sequence of numbers () by treating them as the coefficients of a formal power series. This series is called the generating function of the sequence. Unlike an ordinary series, the ''formal'' power series is not required to converge: in fact, the generating function is not actually regarded as a function, and the "variable" remains an indeterminate. Generating functions were first introduced by Abraham de Moivre in 1730, in order to solve the general linear recurrence problem. One can generalize to formal power series in more than one indeterminate, to encode information about infinite multi-dimensional arrays of numbers. There are various types of generating functions, including ordinary generating functions, exponential generating functions, Lambert series, Bell series, and Dirichlet series; definitions and examples are given below. Every sequence in principle has a generating function of each type (except ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Humbert Polynomials
In mathematics, the Humbert polynomials π(''x'') are a generalization of Pincherle polynomials introduced by given by the generating function :\displaystyle (1-mxt+t^m)^=\sum^\infty _\pi^\lambda_(x)t^n . See also *Umbral calculus In mathematics before the 1970s, the term umbral calculus referred to the surprising similarity between seemingly unrelated polynomial equations and certain "shadowy" techniques used to "prove" them. These techniques were introduced by John Blis ... References * *{{Citation , last1=Humbert , first1=Pierre , title=Some extensions of Pincherle's Polynomials , doi=10.1017/S0013091500035756 , year=1921 , journal=Proceedings of the Edinburgh Mathematical Society , volume=39 , pages=21–24, doi-access=free Polynomials ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
