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GNU Scientific Library Reference Manual - Third Edition (v1.12)
by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. Rossi
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16.11 Error codes

In addition to the standard error codes for invalid arguments the functions can return the following values,

the maximum number of subdivisions was exceeded.
cannot reach tolerance because of roundoff error, or roundoff error was detected in the extrapolation table.
a non-integrable singularity or other bad integrand behavior was found in the integration interval.
the integral is divergent, or too slowly convergent to be integrated numerically.
ISBN 0954612078GNU Scientific Library Reference Manual - Third Edition (v1.12)See the print edition