Open Advanced Search

Log in
Enterprise Plans
Free Trial

Log in
Free Trial
Enterprise Plans
Browse
Features
Pricing

DeepDyve

Advanced Search

show/hide query preview

With all of the words or DOIs:

DeepDyve's default query mode: search by keyword or DOI.

With the exact phrase:

Require these words, in this exact order. Do not surround your terms in double-quotes ("") in this field.

With at least one of the words:

Find any of these words, separated by spaces

Without the words:

Exclude each of these words, separated by spaces

With words in the article title:

Search for these terms only in the title of an article

Published between the years:

With the following authors:

Most effective as: LastName, First Name or Lastname, FN

With words in the journal name:

Search for articles published in journals where these words are in the journal name

Reset filters

Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

DeepDyve requires Javascript to function. Please enable Javascript on your browser to continue.

Theory and Applications of Special Functions

Part of the Developments in Mathematics Book Series (volume 13)

Editors: Ismail, Mourad E.H.; Koelink, Erik

DOI: 10.1007/b104910

ISBN: 978-0-387-24231-6

Publisher: Springer US - Springer Journals

Jan 1, 2005

1 - 10 of 22 Chapters

LitStream

Chapter 1Mizan Rahman, His Mathematics and Literary Writings

Askey, Richard; Ismail, Mourad E.H.; Koelink, Erik

Pages: 1 –28
LitStream

Chapter 2On the Completeness of Sets of q-Bessel Functions Jν(3)(x; q)

Abreu, L. D.; Bustoz, J.

Pages: 29 –38

[We study completeness of systems of third Jackson q-Bessel functions by two quite different methods. The first uses a Dalzell-type criterion and relies on orthogonality and the evaluation of certain q-integrals. The second uses classical entire function theory.]
LitStream

Chapter 3a-Gaussian Polynomials and Finite Rogers-Ramanujan Identities

Andrews, George E.

Pages: 39 –60

[Classical Gaussian polynomials are generalized to two variable polynomials. The first half of the paper is devoted to a full account of this extension and its inherent properties. The final part of the paper considers the role of these polynomials in finite identities of the Rogers-Ramanujan type.]
LitStream

Chapter 4On a Generalized Gamma Convolution Related to the q-Calculus

Berg, Christian

Pages: 61 –76

[We discuss a probability distribution Iq depending on a parameter 0 < q < 1 and determined by its moments n!/(q; q)n. The treatment is purely analytical. The distribution has been discussed recently by Bertoin, Biane and Yor in connection with a study of exponential functionals of Lévy processes.]
LitStream

Chapter 5Ramanujan and Cranks

Berndt, Bruce C.; Chant, Heng Huat; Chan, Song Heng; Liawt, Wen-Chin

Pages: 77 –98

[The existence of the crank was first conjectured by F. J. Dyson in 1944 and was later established by G. E. Andrews and F. C. Garvan in 1987. However, much earlier, in his lost notebook, Ramanujan studied the generating function Fa(q) for the crank and offered several elegant claims about it,...
LitStream

Chapter 6The Saalschütz Chain Reactions and Multiple q-Series Transformations

Wenchang, C H U

Pages: 99 –121

[By recursive use of the q-Saalschütz summation formula, we investigate further the Saalschütz chain reactions introduced by the author in (Chu, 2002). Some general series transformations which express basic terminating series in terms of finite multiple sums will be established. As applications,...
LitStream

Chapter 7Painlevé Equations and Associated Polynomials

Clarkson, Peter A.

Pages: 123 –163

[In this paper we are concerned with rational solutions and associated polynomials for the second, third and fourth Painlevé equations. These rational solutions are expressible as in terms of special polynomials. The structure of the roots of these polynomials is studied and it is shown that...
LitStream

Chapter 8Zeta Functions of Heisenberg Graphs over Finite Rings

DeDeo, Michelle; Martínez, María; Medrano, Archie; Minei, Marvin; Stark, Harold; Terras, Audrey

Pages: 165 –183

[We investigate Ihara-Selberg zeta functions of Cayley graphs for the Heisenberg group over finite rings ℤ/pnℤ, where p is a prime. In order to do this, we must compute the Galois group of the covering obtained by reducing coordinates in ℤ/pn+1ℤ modulo pn+1. The Ihara-Selberg zeta functions of...
LitStream

Chapter 9q-Analogues of Some Multivariable Biorthogonal Polynomials

Gasper, George; Rahman, Mizan

Pages: 185 –208

[In 1989, M. V. Tratnik found a pair of multivariable biorthogonal polynomials Pn(x) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
LitStream

Chapter 10Some Systems of Multivariable Orthogonal Askey-Wilson Polynomials

Gasper, George; Rahman, Mizan

Pages: 209 –219

[In 1991 Tratnik derived two systems of multivariable orthogonal Wilson polynomials and considered their limit cases. q-Analogues of these systems are derived, yielding systems of multivariable orthogonal Askey-Wilson polynomials and their special and limit cases.]

results per page

Browse All eBooks

Features

Search and discover articles on DeepDyve, PubMed, and Google Scholar
Read the full-text of open access and premium content
Organize articles with folders and bookmarks
Collaborate on and share articles and folders

Info

Pricing
Enterprise Plans
Browse Journals & Topics
About DeepDyve

Help

Help
Publishers
Contact Us

Sign up for your 14-Day Free Trial Now!

Read and print from thousands of top scholarly journals.

System error. Please try again!

Continue with Facebook

By signing up, you agree to DeepDyve’s Terms of Service and Privacy Policy.

Already have an account? Log in

Save Article to Bookmarks

Bookmark this article. You can see your Bookmarks on your DeepDyve Library.

To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.

Subscribe to Journal Email Alerts

To subscribe to email alerts, please log in first, or sign up for a DeepDyve account if you don’t already have one.

Follow a Journal

To get new article updates from a journal on your personalized homepage, please log in first, or sign up for a DeepDyve account if you don’t already have one.

Our policy towards the use of cookies

All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.

cookie policy