A q-extension of a partial differential equation and the Hahn polynomials

Zhi Guo Liu

doi:10.1007/s11139-014-9632-1

A q-extension of a partial differential equation and the Hahn polynomials

Zhi Guo Liu^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

Using the theory of analytic functions of several complex variables, we prove that if an analytic function in several variables satisfies a system of $$q$$q-partial differential equations, then, it can be expanded in terms of the product of the homogeneous Hahn polynomials. Some non-trivial applications of this expansion theorem to $$q$$q-series are discussed.

Original language	English
Pages (from-to)	481-501
Number of pages	21
Journal	Ramanujan Journal
Volume	38
Issue number	3
DOIs	https://doi.org/10.1007/s11139-014-9632-1
State	Published - 1 Dec 2015

Keywords

Analytic functions
Hahn polynomials
q-Derivative
q-Identities
q-Integrals
q-Partial differential equations
q-Series

Access to Document

10.1007/s11139-014-9632-1

Cite this

@article{efbafaa88ade447bb3d8da036c976d5a,

title = "A q-extension of a partial differential equation and the Hahn polynomials",

abstract = "Using the theory of analytic functions of several complex variables, we prove that if an analytic function in several variables satisfies a system of \$\$q\$\$q-partial differential equations, then, it can be expanded in terms of the product of the homogeneous Hahn polynomials. Some non-trivial applications of this expansion theorem to \$\$q\$\$q-series are discussed.",

keywords = "Analytic functions, Hahn polynomials, q-Derivative, q-Identities, q-Integrals, q-Partial differential equations, q-Series",

author = "Liu, \{Zhi Guo\}",

note = "Publisher Copyright: {\textcopyright} 2014, Springer Science+Business Media New York.",

year = "2015",

month = dec,

day = "1",

doi = "10.1007/s11139-014-9632-1",

language = "英语",

volume = "38",

pages = "481--501",

journal = "Ramanujan Journal",

issn = "1382-4090",

publisher = "Springer Netherlands",

number = "3",

}

TY - JOUR

T1 - A q-extension of a partial differential equation and the Hahn polynomials

AU - Liu, Zhi Guo

PY - 2015/12/1

Y1 - 2015/12/1

N2 - Using the theory of analytic functions of several complex variables, we prove that if an analytic function in several variables satisfies a system of $$q$$q-partial differential equations, then, it can be expanded in terms of the product of the homogeneous Hahn polynomials. Some non-trivial applications of this expansion theorem to $$q$$q-series are discussed.

AB - Using the theory of analytic functions of several complex variables, we prove that if an analytic function in several variables satisfies a system of $$q$$q-partial differential equations, then, it can be expanded in terms of the product of the homogeneous Hahn polynomials. Some non-trivial applications of this expansion theorem to $$q$$q-series are discussed.

KW - Analytic functions

KW - Hahn polynomials

KW - q-Derivative

KW - q-Identities

KW - q-Integrals

KW - q-Partial differential equations

KW - q-Series

UR - https://www.scopus.com/pages/publications/84947128473

U2 - 10.1007/s11139-014-9632-1

DO - 10.1007/s11139-014-9632-1

M3 - 文章

AN - SCOPUS:84947128473

SN - 1382-4090

VL - 38

SP - 481

EP - 501

JO - Ramanujan Journal

JF - Ramanujan Journal

IS - 3

ER -

A q-extension of a partial differential equation and the Hahn polynomials

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this