Umbral Calculus

ISBN-13: 9783848404452 / Angielski / Miękka / 2012 / 140 str.

Nisar K. S.

Opis

The theory of binomial enumeration is variously called the calculus of finite differences or the Umbral calculus. This theory studies the analogies between various sequences of polynomials pn and the powers sequence xn. The subscript n in pn was thought of as the shadow ("Umbra" means "Shadow" in Latin, whence the name umbral calculus) of the subscript n in xn, and many parallels were discovered between such sequences.At the very outset a brief explanation of the term modern umbral calculus is given. A large part of applied analysis is concerned with the study of certain sequences of special polynomials. Some of the most important of these sequences are associated with the names of Jacobi, Gegenbauer, Legendre, Chebyshev, Bessel, Laguerre, Hermite and Bernoulli. All of these sequences and many more, fall into a special class. Boas and Buck, in their work on polynomial expansions of analytic functions, used the term sequence of generalized Appell type for members of this class.

O autorze

Dr. Nisar K.S has obtained his PhD degree in Applied mathematics from Faculty of Engineering , Aligarh Muslim University, India.He is working in different field of Mathematics like, Special functions, Hypergeometric series, Umbral Calculus and Approximation theory.He is the author of several research papers published in international journals.