In the lost notebook we find a number of identities involving sums of the form
Inasmuch as this sum consists of the terms with positive index taken from the classical Jacobi theta function
, we have chosen to name the series in (6.1.1) partial theta functions. We have chosen the designation partial theta functions, in contrast with L.J. Rogers’s “false theta functions” discussed in Chapters 9 and 11 of our first volume [31, pp. 227–239, 256–259].
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© 2009 Springer-Verlag New York
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Berndt, B.C., Andrews, G.E. (2009). Partial Theta Functions. In: Ramanujan's Lost Notebook. Springer, New York, NY. https://doi.org/10.1007/b13290_7
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DOI: https://doi.org/10.1007/b13290_7
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