Upper and lower bounds on Mathieu characteristic numbers of integer orders

Armando G. M. Neves

doi:10.3934/cpaa.2004.3.447

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2004, Volume 3, Issue 3: 447-464. Doi: 10.3934/cpaa.2004.3.447

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Upper and lower bounds on Mathieu characteristic numbers of integer orders

Armando G. M. Neves^1,

1.
Departamento de Matemática, Universidade Federal de Minas Gerais, Av. Antônio Carlos, 6627 - Caixa Postal 702, 30123-970 - B. Horizonte - MG

Received: February 28, 2003

Revised: February 29, 2004

Published: August 2004

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Abstract

For each Mathieu characteristic number of integer order (MCN) we construct sequences of upper and lower bounds both converging to the MCN. The bounds arise as zeros of polynomials in sequences generated by recursion. This result is based on a constructive proof of convergence for Ince's continued fractions. An important role is also played by the fact that the continued fractions define meromorphic functions.

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Mathematics Subject Classification: 40A15, 30B70, 33E10.

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