### Abstract

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

Pages (from-to) | 1-16 |

Number of pages | 16 |

Journal | Journal of Classical Analysis |

Volume | 1 |

Issue number | 1 |

DOIs | |

State | Published - 2012 |

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### Cite this

*Journal of Classical Analysis*,

*1*(1), 1-16. DOI: 10.7153/jca-01-01

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*Journal of Classical Analysis*, vol 1, no. 1, pp. 1-16. DOI: 10.7153/jca-01-01

**The asymptotics of the mittag-leffler polynomials.** / Paris, Richard B.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The asymptotics of the mittag-leffler polynomials

AU - Paris,Richard B.

PY - 2012

Y1 - 2012

N2 - We investigate the asymptotic behaviour of the Mittag-Leffler polynomials Gn(z) for large n and z, where z is a complex variable satisfying 0 arg z 12 π . A summary of the asymptotic properties of Gn(ix) for real values of x and an approximation for its extreme zeros as n→∞ are given. When the variables are such that z/n is finite, an expansion is obtained using the method of steepest descents applied to a suitable integral representation. This expansion holds everywhere in the first quadrant of the z -plane except in the neighbourhood of the point z=in , where there is a coalescence of saddle points. Numerical results are presented to illustrate the accuracy of the various expansions.

AB - We investigate the asymptotic behaviour of the Mittag-Leffler polynomials Gn(z) for large n and z, where z is a complex variable satisfying 0 arg z 12 π . A summary of the asymptotic properties of Gn(ix) for real values of x and an approximation for its extreme zeros as n→∞ are given. When the variables are such that z/n is finite, an expansion is obtained using the method of steepest descents applied to a suitable integral representation. This expansion holds everywhere in the first quadrant of the z -plane except in the neighbourhood of the point z=in , where there is a coalescence of saddle points. Numerical results are presented to illustrate the accuracy of the various expansions.

U2 - 10.7153/jca-01-01

DO - 10.7153/jca-01-01

M3 - Article

VL - 1

SP - 1

EP - 16

JO - Journal of Classical Analysis

T2 - Journal of Classical Analysis

JF - Journal of Classical Analysis

SN - 1848-5987

IS - 1

ER -