By Dr Mike Hirschhorn

Journal articles

Hirschhorn MD, 1998, 'The sum sqrt 1 + sqrt 2 + ¿ + sqrt n without integration', Australian Mathematical Society Gazette, pp. 143 - 145

Hirschhorn MD, 1998, 'Three classical results or representations of a number', Seminaire Lotharingien de Combinatoire, pp. 41

Hirschhorn MD, 1998, 'Two diophantine equations studied by Ramanujan', Mathematics Magazine, pp. 386 - 388

Hirschhorn MD, 1998, 'Two or three identities of Ramanujan', American Mathematical Monthly, 105, pp. 52 - 54

Hirschhorn MD, 1997, 'Radius of a buried pipe', Australian Mathematical Society Gazette, pp. 180 - 181

Hirschhorn MD, 1997, 'The volume of a cone, without calculus', Mathematics Magazine, pp. 295 - 296

Hirschhorn MD; Sellers JA, 1996, 'Two congruences involving 4-cores', Electronic Journal of Combinatorics, 3, pp. 1 - 8

Hirschhorn MD, 1996, 'A proof in the spirit of Zeilberger of an amazing identity of Ramanujan', Mathematics Magazine, pp. 267 - 269

Hirschhorn MD, 1996, 'A reformulation of Ramanujan`s partition congruences', Journal of Combinatorial Theory Series A, pp. 346 - 347

Hirschhorn MD, 1996, 'Calkin`s binomial identity', Discrete Mathematics, 159, pp. 273 - 278

Hirschhorn MD; Sellers JA, 1996, 'On representations of a number as a sum of three triangles', ACTA Arithmetica, pp. 289 - 301

Hirschhorn MD; Sellers JA, 1996, 'Some amazing facts about 4-cores', Journal of Number Theory, pp. 51 - 69

Hirschhorn MD, 1995, 'A new proof of an old formula', Bulletin of the ICA, 13, pp. 127

Hirschhorn MD, 1995, 'An amazing identity of Ramanujan', Mathematics Magazine, pp. 199 - 201

Hirschhorn MD, 1994, 'Ramanujan's partition congruences', Discrete Mathematics, 131, pp. 351 - 355, http://dx.doi.org/10.1016/0012-365X(94)90397-2

Hirschhorn MD, 1994, 'Several Identities in Statistical Mechanics', International Journal of Mathematics and Mathematical Sciences, 17, pp. 817 - 820, http://dx.doi.org/10.1155/S0161171294001146

Hirschhorn MD, 1993, 'On the parity of p(n), II', Journal of Combinatorial Theory, Series A, 62, pp. 128 - 138, http://dx.doi.org/10.1016/0097-3165(93)90075-J

Hirschhorn MD, 1988, 'A generalisation of the quintuple product identity', Journal of the Australian Mathematical Society, 44, pp. 42 - 45, http://dx.doi.org/10.1017/S1446788700031359

Hirschhorn MD, 1987, 'A simple proof of Jacobi's four-square theorem', Proceedings of the American Mathematical Society, 101, pp. 436 - 438, http://dx.doi.org/10.1090/S0002-9939-1987-0908644-9

Hirschhorn MD; Hunt DC, 1985, 'Equilateral convex pentagons which tile the plane', Journal of Combinatorial Theory, Series A, 39, pp. 1 - 18, http://dx.doi.org/10.1016/0097-3165(85)90078-0

Guttmann AJ; Hirschhorn M, 1984, 'Comment on the number of spiral self-avoiding walks', Journal of Physics A: General Physics, 17, pp. 3613 - 3614, http://dx.doi.org/10.1088/0305-4470/17/18/029

Hirschhorn MD, 1983, 'A Simple proof of an identity of Ramanujan', Journal of the Australian Mathematical Society, 34, pp. 31 - 35, http://dx.doi.org/10.1017/S1446788700019728

Hirschhorn MD, 1982, 'A Simple Proof of Jacobi’s Four-Square Theorem', Journal of the Australian Mathematical Society, 32, pp. 61 - 67, http://dx.doi.org/10.1017/S144678870002440X

Hirschhorn MD; Hunt DC, 1981, 'A simple proof of the Ramanujan conjecture for powers of 5', Journal fur die Reine und Angewandte Mathematik, 1981, pp. 1 - 17, http://dx.doi.org/10.1515/crll.1981.326.1

Hirschhorn MD, 1981, 'Infinitely many identities of kolberg type', Journal of the Australian Mathematical Society, 31, pp. 20 - 25, http://dx.doi.org/10.1017/S1446788700018450

Hirschhorn MD, 1980, 'A continued fraction of ramanujan', Journal of the Australian Mathematical Society, 29, pp. 80 - 86, http://dx.doi.org/10.1017/S1446788700020954

Hirschhorn MD, 1980, 'Two further ramanujan pairs', Journal of the Australian Mathematical Society, 30, pp. 1 - 4, http://dx.doi.org/10.1017/S1446788700021856

Hirschhorn MD, 1979, 'Some partition theorems of the Rogers-Ramanujan type', Journal of Combinatorial Theory, Series A, 27, pp. 33 - 37, http://dx.doi.org/10.1016/0097-3165(79)90005-0

Hirschhorn MD, 1976, 'Simple proofs of identities of MacMahon and Jacobi', Discrete Mathematics, 16, pp. 161 - 162, http://dx.doi.org/10.1016/0012-365X(76)90144-8

Hirschhorn MD; Loxton JH, 1975, 'Congruence properties of the binary partition function', Mathematical Proceedings of the Cambridge Philosophical Society, 78, pp. 437 - 442, http://dx.doi.org/10.1017/S0305004100051896

Hirschhorn MD, 1974, 'A continued fraction', Duke Mathematical Journal, 41, pp. 27 - 33, http://dx.doi.org/10.1215/S0012-7094-74-04104-0

Hirschhorn MD, 1973, 'A continued fraction of Carlitz', Duke Mathematical Journal, 40, pp. 77 - 80, http://dx.doi.org/10.1215/S0012-7094-73-04008-8

Hirschhorn MD, 1972, 'Partitions and ramanujan’s continued fraction', Duke Mathematical Journal, 39, pp. 789 - 791, http://dx.doi.org/10.1215/S0012-7094-72-03986-5

Conference Papers

Hirschhorn MD, 2016, 'Ramanujan’s tau function', in Springer Proceedings in Mathematics and Statistics, Gainesville, FL, USA, pp. 311 - 328, presented at Analytic Number Theory, Modular Forms and q-Hypergeometric Series, Gainesville, FL, USA, 17 March 2016 - 21 March 2016, http://dx.doi.org/10.1007/978-3-319-68376-8_18

Hirschhorn MD; Mcgowan JA, 1999, 'Algebraic consequences of Jacobi`s two- and four-square theorems', in Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics, University of Florida, Gainesville, presented at Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics, University of Florida, Gainesville, 11 November 1999 - 13 November 1999

Hirschhorn MD; Sellers JA, 1999, 'Some relations for partitions into four squares', in international workshop special functions, Hong Kong, presented at international workshop special functions, Hong Kong, 21 June 1999 - 25 June 1999

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