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Solutions of first level of meromorphic differential equations

Published online by Cambridge University Press:  20 January 2009

W. Balser
W. Balser
Affiliation:
Abt. Mathematik V, Universität Ulm, D-7900 Ulm, West Germany
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Let a meromorphic differential equation

be given, where r is an integer, and the series converges for |z| sufficiently large. Then it is well known that (0.1) is formally satisfied by an expression

where F( z) is a formal power series in z–1 times an integer power of z, and F( z) has an inverse of the same kind, L is a constant matrix, and

is a diagonal matrix of polynomials qj( z) in a root of z, 1≦ j≦ n. If, for example, all the polynomials in Q( z) are equal, then F( z) can be seen to be a convergent series (see Section 1), whereas if not, then generally the coefficients in F( z) grow so rapidly that F( z) diverges for every (finite) z.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 25 , Issue 2 , June 1982 , pp. 183 - 207
Copyright
Copyright © Edinburgh Mathematical Society 1982

References

REFERENCES

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