### Abstract

Original language | English |
---|---|

Pages (from-to) | 82–105 |

Number of pages | 24 |

Journal | Lithuanian Mathematical Journal |

Volume | 54 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2014 |

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### Cite this

*Lithuanian Mathematical Journal*,

*54*(1), 82–105. https://doi.org/10.1007/s10986-014-9229-9

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*Lithuanian Mathematical Journal*, vol. 54, no. 1, pp. 82–105. https://doi.org/10.1007/s10986-014-9229-9

**Exponentially small expansions of the Wright function on the Stokes lines.** / Paris, Richard B.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Exponentially small expansions of the Wright function on the Stokes lines

AU - Paris, Richard B.

PY - 2014/1

Y1 - 2014/1

N2 - We investigate a particular aspect of the asymptotic expansion of the Wright function pΨq(z) for large |z|. In the case p = 1, q ⩾ 0, we establish the form of the exponentially small expansion of this function on certain rays in the z-plane (known as Stokes lines). The importance of such exponentially small terms is encountered in analytic probability theory and in the theory of generalised linear models. In addition, the transition of the Stokes multiplier connected with the subdominant exponential expansion across the Stokes lines is shown to obey the familiar error-function smoothing law expressed in terms of an appropriately scaled variable. Some numerical examples which confirm the accuracy of the expansion are given.

AB - We investigate a particular aspect of the asymptotic expansion of the Wright function pΨq(z) for large |z|. In the case p = 1, q ⩾ 0, we establish the form of the exponentially small expansion of this function on certain rays in the z-plane (known as Stokes lines). The importance of such exponentially small terms is encountered in analytic probability theory and in the theory of generalised linear models. In addition, the transition of the Stokes multiplier connected with the subdominant exponential expansion across the Stokes lines is shown to obey the familiar error-function smoothing law expressed in terms of an appropriately scaled variable. Some numerical examples which confirm the accuracy of the expansion are given.

U2 - 10.1007/s10986-014-9229-9

DO - 10.1007/s10986-014-9229-9

M3 - Article

VL - 54

SP - 82

EP - 105

JO - Lithuanian Mathematical Journal

JF - Lithuanian Mathematical Journal

SN - 0363-1672

IS - 1

ER -