REMARKS FOR BASIC APPELL SERIES

Multiple Hypergeometric Series – Appell Series and Beyond

This survey article (which will appear as a chapter in the book “Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions”, Springer-Verlag) provides a small collection of basic material on multiple hypergeometric series of Appell-type and of more general series of related type.

Appell Sequences, Continuous Wavelet Transforms and Series Expansions

A series expansion with remainder for functions in a Sobolev space is derived in terms of the classical Bernoulli polynomials, the B-spline scale-space and the continuous wavelet transforms with the derivatives of the standardized B-splines as mother wavelets. In the limit as their orders tend to infinity, the B-splines and their derivatives converge to the Gaussian function and its derivatives...

Turan’s Inequality for Appell Polynomials

Some Remarks on Infinite Series

In the present paper we investigate the following problems. Suppose an >O for n_-I and Z a,=-. n=1 N° 1. Does there exist a sequence of natural numbers No =O, Ni l-, such that it decomposes the series monotone decreasingly : In order to state the second problem we define the index nk (c) as the minimum m such that (2) Now the second problem is as follows. are equiconvergent. m kc a j. j=1 N° 2....

Basic Hypergeometric Series

Abstract. We compute the inverse of a specific infinite r-dimensional matrix, thus unifying multidimensional matrix inversions recently found by Milne, Lilly, and Bhatnagar. Our inversion is an r-dimensional extension of a matrix inversion previously found by Krattenthaler. We also compute the inverse of another infinite r-dimensional matrix. As applications of our matrix inversions, we derive ...