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Numerical investigation of certain asymptotic results in the theory of partitions

Authors: M. S. Cheema and W. E. Conway
Journal: Math. Comp. 26 (1972), 999-1005
MSC: Primary 10A45; Secondary 10-04, 10J20
MathSciNet review: 0314756
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Abstract: A numerical investigation of some of the asymptotic formulas in partitions is made. Comparisons with actual computed values show that in certain cases only the relative error tends to zero and the errors are significant. Only in the case of $ {p_k}(n)$ is it found that only a few terms of the asymptotic series are sufficient to obtain the exact value.

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Keywords: Generating functios, $ k$-line partitions, plane partitions, asymptotic formulas, modular functions, relative errors, Bernoulli numbers
Article copyright: © Copyright 1972 American Mathematical Society

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