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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] |
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] |
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] |
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] |
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 Blissard and are sometimes called Blissard's symbolic method. They are often attributed to Édouard Lucas (or James Joseph Sylvester), who used the technique extensively. Short history In the 1930s and 1940s, Eric Temple Bell attempted to set the umbral calculus on a rigorous footing. In the 1970s, Steven Roman, Gian-Carlo Rota, and others developed the umbral calculus by means of linear functionals on spaces of polynomials. Currently, ''umbral calculus'' refers to the study of Sheffer sequences, including polynomial sequences of binomial type and Appell sequences, but may encompass systematic correspondence techniques of the calculus of finite differences. The 19th-century umbral calculus The method is a notational procedure used for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer-Verlag
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
