Exponentially small expansions in the asymptotics of the Wright function

Richard B. Paris

Research output: Contribution to journal › Article

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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

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Wright Function
Generalized Hypergeometric Function
Numerical Examples
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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.
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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

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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.

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DO - 10.1016/j.cam.2009.12.040

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JO - Journal of Computational and Applied Mathematics

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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

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