Third Order Mock Theta Functions: Partial Fraction Expansions

George E. Andrews and Bruce C. Berndt
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George E. Andrews: The Pennsylvania State University, Department of Mathematics
Bruce C. Berndt: University of Illinois, Department of Mathematics

Chapter 4 in Ramanujan's Lost Notebook, 2018, pp 35-58 from Springer

Abstract: Abstract Partial fractions arise again and again in the Lost Notebook. Indeed, we have already seen instances of partial fractions (e.g. [32, p. 271]) that specialize to mock theta functions. On pages 2 and 17 in his Lost Notebook [232], Ramanujan recorded four identities involving the rank generating function. Of course, Ramanujan would not have used this terminology, because the rank of a partition was not defined until 1944 by F.J. Dyson Dyson, F.J. [130]. He defined the rank of a partition to be the largest rank of a partition part minus the number of parts.

Date: 2018
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DOI: 10.1007/978-3-319-77834-1_4

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