Numerical investigation of certain asymptotic results in the theory of partitions

Cheema, M. S.; Conway, W. E.

doi:10.1090/S0025-5718-1972-0314756-0

Numerical investigation of certain asymptotic results in the theory of partitions
HTML articles powered by AMS MathViewer

by M. S. Cheema and W. E. Conway PDF

Math. Comp. 26 (1972), 999-1005 Request permission

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.

References

M. S. Cheema and C. T. Haskell, Multirestricted and rowed partitions, Duke Math. J. 34 (1967), 443–451. MR 217030
J. M. Gandhi, Generalization of a certain function related to the partition function, Mathematica (Cluj) 11(34) (1969), 245–251. MR 260692
Basil Gordon and Lorne Houten, Notes on plane partitions. III, Duke Math. J. 36 (1969), 801–824. MR 248104
Basil Gordon and Lorne Houten, Notes on plane partitions. I, II, J. Combinatorial Theory 4 (1968), 72–80; 81–99. MR 218252, DOI 10.1017/s000708740000340x

Proc. London Math. Soc.

Percy A. MacMahon, Combinatory analysis, Chelsea Publishing Co., New York, 1960. Two volumes (bound as one). MR 0141605
D. H. Lehmer, On the series for the partition function, Trans. Amer. Math. Soc. 43 (1938), no. 2, 271–295. MR 1501943, DOI 10.1090/S0002-9947-1938-1501943-5
Hans Rademacher, On the Selberg formula for $A_k(n)$, J. Indian Math. Soc. (N.S.) 21 (1957), 41–55 (1958). MR 92818
Albert Leon Whiteman, A sum connected with the series for the partition function, Pacific J. Math. 6 (1956), 159–176. MR 80122
Albert Leon Whiteman, A sum connected with the partition function, Bull. Amer. Math. Soc. 53 (1947), 598–603. MR 20590, DOI 10.1090/S0002-9904-1947-08847-9

Quart. J. Math.