A constructive method for plane-wave representations of special functions
File(s)
Accepted version
Published version
Author(s)
Crowdy, DG
Type
Journal Article
Abstract
A general constructive scheme for the derivation of plane-wave representations
of special functions is proposed. Illustrative examples of the construction are
given. As one case study, new integral representations of the elliptic Weierstrass
℘ function are derived; these complement, and generalize, similar new planewave
integral representations of the same function recently found by Dienstfrey
& Huang [J. Math. Anal. Appl., 316, 142–160, (2006)] using other techniques.
Our approach is inspired by recent developments in the so-called Fokas transform
for the solution of boundary value problems for partial differential equations.
Keywords: plane wave representation, elliptic function, transform method,
special functions
of special functions is proposed. Illustrative examples of the construction are
given. As one case study, new integral representations of the elliptic Weierstrass
℘ function are derived; these complement, and generalize, similar new planewave
integral representations of the same function recently found by Dienstfrey
& Huang [J. Math. Anal. Appl., 316, 142–160, (2006)] using other techniques.
Our approach is inspired by recent developments in the so-called Fokas transform
for the solution of boundary value problems for partial differential equations.
Keywords: plane wave representation, elliptic function, transform method,
special functions
Date Issued
2015-12-03
Date Acceptance
2015-11-03
Citation
Journal of Mathematical Analysis and Applications, 2015, 436 (1), pp.149-167
ISSN
0022-247X
Publisher
Elsevier
Start Page
149
End Page
167
Journal / Book Title
Journal of Mathematical Analysis and Applications
Volume
436
Issue
1
Copyright Statement
© 2015 The Author. Published by Elsevier Inc. This is an open access article
under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
License URL
Sponsor
Engineering & Physical Science Research Council (EPSRC)
The Royal Society
Grant Number
EP/K019430/1
WM120037
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
Plane-wave representation
Elliptic function
Transform method
Special functions
PARTIAL-DIFFERENTIAL-EQUATIONS
INTEGRAL-REPRESENTATIONS
CIRCULAR DOMAINS
TRANSFORM METHOD
LATTICE SUMS
POLYGON
General Mathematics
0101 Pure Mathematics
0102 Applied Mathematics
0906 Electrical And Electronic Engineering
Publication Status
Published