# American Institute of Mathematical Sciences

September  2004, 3(3): 447-464. doi: 10.3934/cpaa.2004.3.447

## Upper and lower bounds on Mathieu characteristic numbers of integer orders

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

Received  March 2003 Revised  March 2004 Published  June 2004

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.
Citation: Armando G. M. Neves. Upper and lower bounds on Mathieu characteristic numbers of integer orders. Communications on Pure & Applied Analysis, 2004, 3 (3) : 447-464. doi: 10.3934/cpaa.2004.3.447
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