On the orthogonality of the MacDonald's functions

A. Passian; H. Simpson; S. Kouchekian; S. B. Yakubovich

doi:10.1016/j.jmaa.2009.06.067

On the orthogonality of the MacDonald's functions

A. Passian
, H. Simpson
, S. Kouchekian
, S. B. Yakubovich

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

18 Scopus citations

Abstract

A proof of an orthogonality relation for the MacDonald's functions with identical arguments but unequal complex lower indices is presented. The orthogonality is derived first via a heuristic approach based on the Mehler-Fock integral transform of the MacDonald's functions, and then proved rigorously using a polynomial approximation procedure.

Original language	English
Pages (from-to)	380-390
Number of pages	11
Journal	Journal of Mathematical Analysis and Applications
Volume	360
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2009.06.067
State	Published - Dec 15 2009

Funding

E-mail addresses: [email protected] (A. Passian), [email protected] (H. Simpson), [email protected] (S. Kouchekian), [email protected] (S.B. Yakubovich). 1 The work of the first author was supported by the Oak Ridge National Laboratory, Managed by UT-Battelle, LLC for the Department of Energy under contract number DE-AC05-0096OR22725. 2 The research of the third author was partially supported by the National Science Foundation grant DMS–0500916. 3 The work of the fourth author was supported by the “Centro de Mathematica” of the University of Porto.

Keywords

Kontorovich-Lebedev transform
Mehler-Fock transform
Modified Bessel functions

Access to Document

10.1016/j.jmaa.2009.06.067

Cite this

@article{3f17d2659eb947f79797ed0ad4be8f07,

title = "On the orthogonality of the MacDonald's functions",

abstract = "A proof of an orthogonality relation for the MacDonald's functions with identical arguments but unequal complex lower indices is presented. The orthogonality is derived first via a heuristic approach based on the Mehler-Fock integral transform of the MacDonald's functions, and then proved rigorously using a polynomial approximation procedure.",

keywords = "Kontorovich-Lebedev transform, Mehler-Fock transform, Modified Bessel functions",

author = "A. Passian and H. Simpson and S. Kouchekian and Yakubovich, \{S. B.\}",

year = "2009",

month = dec,

day = "15",

doi = "10.1016/j.jmaa.2009.06.067",

language = "English",

volume = "360",

pages = "380--390",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Elsevier",

number = "2",

}

TY - JOUR

T1 - On the orthogonality of the MacDonald's functions

AU - Passian, A.

AU - Simpson, H.

AU - Kouchekian, S.

AU - Yakubovich, S. B.

PY - 2009/12/15

Y1 - 2009/12/15

N2 - A proof of an orthogonality relation for the MacDonald's functions with identical arguments but unequal complex lower indices is presented. The orthogonality is derived first via a heuristic approach based on the Mehler-Fock integral transform of the MacDonald's functions, and then proved rigorously using a polynomial approximation procedure.

AB - A proof of an orthogonality relation for the MacDonald's functions with identical arguments but unequal complex lower indices is presented. The orthogonality is derived first via a heuristic approach based on the Mehler-Fock integral transform of the MacDonald's functions, and then proved rigorously using a polynomial approximation procedure.

KW - Kontorovich-Lebedev transform

KW - Mehler-Fock transform

KW - Modified Bessel functions

UR - https://www.scopus.com/pages/publications/70349381450

U2 - 10.1016/j.jmaa.2009.06.067

DO - 10.1016/j.jmaa.2009.06.067

M3 - Article

AN - SCOPUS:70349381450

SN - 0022-247X

VL - 360

SP - 380

EP - 390

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

On the orthogonality of the MacDonald's functions

Abstract

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this