Probabilities as Values of Modular Forms and Continued Fractions
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2009/941920 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |