Book Review
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MathSciNet review:
1567360
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Book Information:
Author:
Leonard Lewin
Title:
Polylogarithms and associated functions
Additional book information:
North-Holland, Amsterdam, 1981, xvii + 359 pp., $54.95.
1. N. H. Abel, Note sur la fonction ψx = x + x, Oeuvres complètes de Niels Hendrik Abel, Tome second, Christiania 1881; reprinted by Johnson Reprint Corp., New York, 1973, pp. 189-193.
Spencer J. Bloch, Higher regulators, algebraic $K$-theory, and zeta functions of elliptic curves, CRM Monograph Series, vol. 11, American Mathematical Society, Providence, RI, 2000. MR 1760901, DOI 10.1090/crmm/011
Spencer Bloch, The dilogarithm and extensions of Lie algebras, Algebraic $K$-theory, Evanston 1980 (Proc. Conf., Northwestern Univ., Evanston, Ill., 1980) Lecture Notes in Math., vol. 854, Springer, Berlin-New York, 1981, pp. 1–23. MR 618298, DOI 10.1007/BFb0089515
4. T. Clausen, Veber die Function sin φ + l/22sin 2φ + l/32sin3φ + etc., J. Reine Angew. Math. 8(1932), 298-300.
L. Lewin, Dilogarithms and associated functions, Macdonald, London, 1958. Foreword by J. C. P. Miller. MR 0105524
6. N. Lobachevsky, Imaginary geometry and its application to integration, Kasan, 1836 (Russian); German translation in N. J. Lobatschefskij's Imaginäre Geometrie und Anwendung der imaginären Geometrie auf einige Integrale, transl, by H. Liebmann, Abhand. Gesch. Math. (Leipzig) 19 (1904).
7. L. Schläfli, On the multiple integral fn dx dy • • • dz, whose limits are p1 = a1x + b1y + • • • + h1z > 0, p2 > 0,• • •,pn >0, and x2 + y2 + • • • + z2 < 1, Quart. J. Math. 2 (1858), 269-301; 3 (1860), 54-68, 97-108. Reprinted in Gesammelte Mathematische Abhandlungen, Band II, Birkhäuser, Basel, 1953, pp. 219-270.
8. W. Spence, An essay on the theory of the various orders of logarithmic transcendents, London and Edinburgh, 1809.
9. W. Spence, Mathematical essays (J. F. W. Herschel, ed. ), London, 1820.
10. W. Spence, Amer. Math. Monthly 88 (1981), 713.
11. W. Thurston, Geometry and topology of 3-manifolds, Chapter 7, "Computation of volume", notes by J. W. Milnor, Lecture notes, Princeton, N. J.
- 1.
- N. H. Abel, Note sur la fonction ψx = x + x, Oeuvres complètes de Niels Hendrik Abel, Tome second, Christiania 1881; reprinted by Johnson Reprint Corp., New York, 1973, pp. 189-193.
- 2.
- S. Bloch, Higher regulators, algebraic K-theory, and zeta functions of elliptic curves, Lecture notes, Univ. of California, Irvine, 1978 (preprint). MR 1760901
- 3.
- S. Bloch, The dilogarithm and extensions of Lie algebras, Algebraic K-theory (Evanston, 1980), (E. M. Friedlander and M. R. Stein, eds. ), Lecture Notes in Math., vol. 854, Springer-Verlag, Berlin, Heidelberg and New York, 1981, pp. 1-23. MR 618298
- 4.
- T. Clausen, Veber die Function sin φ + l/22sin 2φ + l/32sin3φ + etc., J. Reine Angew. Math. 8(1932), 298-300.
- 5.
- L. Lewin, Dilogarithms and associated functions, Macdonald, London, 1958. MR 105524
- 6.
- N. Lobachevsky, Imaginary geometry and its application to integration, Kasan, 1836 (Russian); German translation in N. J. Lobatschefskij's Imaginäre Geometrie und Anwendung der imaginären Geometrie auf einige Integrale, transl, by H. Liebmann, Abhand. Gesch. Math. (Leipzig) 19 (1904).
- 7.
- L. Schläfli, On the multiple integral fn dx dy • • • dz, whose limits are p1 = a1x + b1y + • • • + h1z > 0, p2 > 0,• • •,pn >0, and x2 + y2 + • • • + z2 < 1, Quart. J. Math. 2 (1858), 269-301; 3 (1860), 54-68, 97-108. Reprinted in Gesammelte Mathematische Abhandlungen, Band II, Birkhäuser, Basel, 1953, pp. 219-270.
- 8.
- W. Spence, An essay on the theory of the various orders of logarithmic transcendents, London and Edinburgh, 1809.
- 9.
- W. Spence, Mathematical essays (J. F. W. Herschel, ed. ), London, 1820.
- 10.
- W. Spence, Amer. Math. Monthly 88 (1981), 713.
- 11.
- W. Thurston, Geometry and topology of 3-manifolds, Chapter 7, "Computation of volume", notes by J. W. Milnor, Lecture notes, Princeton, N. J.
Review Information:
Reviewer:
Richard Askey
Journal:
Bull. Amer. Math. Soc.
6 (1982), 248-251
DOI:
https://doi.org/10.1090/S0273-0979-1982-14998-9
