Probabilities as Values of Modular Forms and Continued Fractions

Riad Masri and Ken Ono

International Journal of Mathematics and Mathematical Sciences, 2009, vol. 2009, 1-11

Abstract:

We consider certain probability problems which are naturally related to integer partitions. We show that the corresponding probabilities are values of classical modular forms. Thanks to this connection, we then show that certain ratios of probabilities are specializations of the Rogers-Ramanujan and Ramanujan- Selberg- Gordon-Göllnitz continued fractions. One particular evaluation depends on a result from Ramanujan's famous first letter to Hardy.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:941920

DOI: 10.1155/2009/941920

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