On a nonlinear relation for computing the overpartition function

References

[1] Andrews, G. E.—Eriksson, K.: Integer partitions, Cambridge University Press, Cambridge, 2004.10.1017/CBO9781139167239Search in Google Scholar

[2] Andrews, G. E.: Singular overpartitions, Int. J. Number Theory 11(5) (2015), 1523–1533.10.1142/S1793042115400059Search in Google Scholar

[3] Bessenrodt, C.: On pairs of partitions with steadily decreasing parts, J. Combin. Theory Ser. A 99 (2002), 162–174.10.1006/jcta.2002.3267Search in Google Scholar

[4] Bringmann, K.—Lovejoy, J.: Dyson's rank, overpartitions, and weak Maass forms, Int. Math. Res. Not. IMRN, (2007), rnm063.10.1093/imrn/rnm063Search in Google Scholar

[5] Chen, S.-C.: On the number of overpartitions into odd parts, Discrete Math., 325 (2014), 32–37.10.1016/j.disc.2014.02.015Search in Google Scholar

[6] Chen, W. Y. C.—Zhao, J. J. Y.: The Gaussian coefficients and overpartitions, Discrete Math. 305 (2005), 350–353.10.1016/j.disc.2005.06.025Search in Google Scholar

[7] Corteel, S.—Lovejoy, J.: Overpartitions, Trans. Amer. Math. Soc. 356 (2004), 1623–1635.10.1090/S0002-9947-03-03328-2Search in Google Scholar

[8] Corteel, S.—Hitczenko, P.: Multiplicity and number of parts in overpartitions, Ann. Comb. 8(3) (2004), 287–301.10.1007/s00026-004-0221-7Search in Google Scholar

[9] Corteel, S.—Goh, W. M. Y.—Hitczenko, P.: A local limit theorem in the theory of overpartitions, Algorithmica 46 (2006), 329–343.10.1007/s00453-006-0102-zSearch in Google Scholar

[10] Corteel, S.—Mallet, O.: Overpartitions, lattice paths, and Rogers-Ramanujan identities, J. Combin. Theory Ser. A, 114(8) (2007), 1407–1437.10.1016/j.jcta.2007.02.004Search in Google Scholar

[11] Fortin, J.-F.—Jacob, P.—Mathieu, P.: Jagged partitions, Ramanujan J. 10 (2005), 215–235.10.1007/s11139-005-4848-8Search in Google Scholar

[12] Fu, A. M.—Lascoux, A.: q-identities related to overpartitions and divisor functions, Electron. J. Combin., 12 (2005), RP38.10.37236/1935Search in Google Scholar

[13] Hardy, G. H.—Ramanujan, S.: Asymptotic formulae in combinatory analysis, Proceedings of the London Mathematical Society (2) 17 (1918), 75–115.10.1112/plms/s2-17.1.75Search in Google Scholar

[14] Hirschhorn, M. D.—Sellers, J. A.: Arithmetic relations for overpartitions, J. Combin. Math. Combin. Comp. 53 (2005), 65–73.Search in Google Scholar

[15] Hirschhorn, M. D.—Sellers, J. A.: Arithmetic Properties of Overpartitions into Odd Parts, Ann. Comb. 10(3) (2006), 353–367.10.1007/s00026-006-0293-7Search in Google Scholar

[16] Johansson, F.: Efficient implementation of the Hardy–Ramanujan–Rademacher formula, LMS J. Comput. Math. 15(1) (2012), 341–359.10.1112/S1461157012001088Search in Google Scholar

[17] Kim, B.: A short note on the overpartition function, Discrete Math. 309 (2009), 2528–2532.10.1016/j.disc.2008.05.007Search in Google Scholar

[18] Lebesgue, V. A.: Sommation de quelques séries, J. Math. Pure. Appl. 5 (1840), 42–71.Search in Google Scholar

[19] Lovejoy, J.: Gordon's theorem for overpartitions, J. Comb. Theory Ser. A 103 (2003), 393–401.10.1016/S0097-3165(03)00116-XSearch in Google Scholar

[20] Lovejoy, J.: Overpartition theorems of the Rogers-Ramanujan type, J. London Math. Soc. 69 (2004), 562–574.10.1112/S0024610704005216Search in Google Scholar

[21] Lovejoy, J.: Overpartitions and real quadratic fields, J. Number Theory 106 (2004), 178–186.10.1016/j.jnt.2003.12.014Search in Google Scholar

[22] Lovejoy, J.: A theorem on seven-colored overpartitions and its applications, Int. J. Number Theory 1 (2005), 215–224.10.1142/S1793042105000157Search in Google Scholar

[23] Lovejoy, J.: Rank and conjugation for the Frobenius representation of an overpartition, Ann. Comb. 9 (2005), 321–334.10.1007/s00026-005-0260-8Search in Google Scholar

[24] Lovejoy, J.: Partitions and overpartitions with attached parts, Arch. Math. (Basel) 88 (2007), 316–322.10.1007/s00013-006-1978-1Search in Google Scholar

[25] Mahlburg, K.: The overpartition function modulo small powers of 2, Discrete Math. 286 (2004), 263–267.10.1016/j.disc.2004.03.014Search in Google Scholar

[26] Merca, M.: On the arithmetic mean of the square roots of the first n positive integers, College Math. J. 48 (2017), 129–133.10.4169/college.math.j.48.2.129Search in Google Scholar

[27] Merca, M.: From a Rogers's identity to overpartitions, Period. Math. Hungar. 75 (2017), 172–179.10.1007/s10998-016-0180-xSearch in Google Scholar

[28] Merca, M.—Wang, C.—Yee, A. J.: A truncated theta identity of Gauss and overpartitions into odd parts, Ann. Comb. 23 (2019), 907–915.10.1007/978-3-030-57050-7_30Search in Google Scholar

[29] Santos, J. P. O.—Sills, A. V.: q-Pell sequences and two identities of V.A. Lebesgue, Discrete Math. 257(1) (2002), 125–142.10.1016/S0012-365X(01)00475-7Search in Google Scholar

[30] Sills, A. V.: A Rademacher type formula for partitions and overpartitions, Int. J. Math. Math. Sci. (2010), Article ID 630458.10.1155/2010/630458Search in Google Scholar

[31] Zuckerman, H. S.: On the coefficients of certain modular forms belonging to subgroups of the modular group, Trans. Amer. Math. Soc. 45 (1939), 298–321.10.1090/S0002-9947-1939-1501993-XSearch in Google Scholar