Exponentially small expansions in the asymptotics of the Wright function

Richard B. Paris

Research output: Contribution to journal › Article

10 Citations (Scopus)
11 Downloads (Pure)

Abstract

We consider exponentially small expansions present in the asymptotics of the generalised hypergeometric function, or Wright function, pΨq(z) for large |z| that have not been considered in the existing theory. Our interest is principally with those functions of this class that possess either a finite algebraic expansion or no such expansion and with parameter values that produce exponentially small expansions in the neighbourhood of the negative real z axis. Numerical examples are presented to demonstrate the presence of these exponentially small expansions.
Original languageEnglish
Pages (from-to)488-504
Number of pages17
JournalJournal of Computational and Applied Mathematics
Volume234
Issue number2
DOIs
Publication statusPublished - May 2010

Fingerprint

Wright Function
Generalized Hypergeometric Function
Numerical Examples
Demonstrate

Cite this

Paris, Richard B. / Exponentially small expansions in the asymptotics of the Wright function. In: Journal of Computational and Applied Mathematics. 2010 ; Vol. 234, No. 2. pp. 488-504.
@article{1fc232b320f34bb5be8f828a0b8f46b7,
title = "Exponentially small expansions in the asymptotics of the Wright function",
abstract = "We consider exponentially small expansions present in the asymptotics of the generalised hypergeometric function, or Wright function, pΨq(z) for large |z| that have not been considered in the existing theory. Our interest is principally with those functions of this class that possess either a finite algebraic expansion or no such expansion and with parameter values that produce exponentially small expansions in the neighbourhood of the negative real z axis. Numerical examples are presented to demonstrate the presence of these exponentially small expansions.",
author = "Paris, {Richard B.}",
year = "2010",
month = "5",
doi = "10.1016/j.cam.2009.12.040",
language = "English",
volume = "234",
pages = "488--504",
journal = "Journal of Computational and Applied Mathematics",
issn = "0377-0427",
publisher = "Elsevier",
number = "2",

}

Paris, RB 2010, 'Exponentially small expansions in the asymptotics of the Wright function', Journal of Computational and Applied Mathematics, vol. 234, no. 2, pp. 488-504. https://doi.org/10.1016/j.cam.2009.12.040

Exponentially small expansions in the asymptotics of the Wright function. / Paris, Richard B.

In: Journal of Computational and Applied Mathematics, Vol. 234, No. 2, 05.2010, p. 488-504.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Exponentially small expansions in the asymptotics of the Wright function

AU - Paris, Richard B.

PY - 2010/5

Y1 - 2010/5

N2 - We consider exponentially small expansions present in the asymptotics of the generalised hypergeometric function, or Wright function, pΨq(z) for large |z| that have not been considered in the existing theory. Our interest is principally with those functions of this class that possess either a finite algebraic expansion or no such expansion and with parameter values that produce exponentially small expansions in the neighbourhood of the negative real z axis. Numerical examples are presented to demonstrate the presence of these exponentially small expansions.

AB - We consider exponentially small expansions present in the asymptotics of the generalised hypergeometric function, or Wright function, pΨq(z) for large |z| that have not been considered in the existing theory. Our interest is principally with those functions of this class that possess either a finite algebraic expansion or no such expansion and with parameter values that produce exponentially small expansions in the neighbourhood of the negative real z axis. Numerical examples are presented to demonstrate the presence of these exponentially small expansions.

U2 - 10.1016/j.cam.2009.12.040

DO - 10.1016/j.cam.2009.12.040

M3 - Article

VL - 234

SP - 488

EP - 504

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 2

ER -

Paris RB. Exponentially small expansions in the asymptotics of the Wright function. Journal of Computational and Applied Mathematics. 2010 May;234(2):488-504. https://doi.org/10.1016/j.cam.2009.12.040

Access to Document