TY - JOUR A2 - Haukkanen, Pentti AU - Masri, Riad AU - Ono, Ken PY - 2009 DA - 2009/09/15 TI - Probabilities as Values of Modular Forms and Continued Fractions SP - 941920 VL - 2009 AB - We consider certain probability problems which are naturally related tointeger partitions. We show that the corresponding probabilities are values of classicalmodular forms. Thanks to this connection, we then show that certain ratios ofprobabilities are specializations of the Rogers-Ramanujan and Ramanujan- Selberg-Gordon-Göllnitz continued fractions. One particular evaluation depends on a resultfrom Ramanujan's famous first letter to Hardy. SN - 0161-1712 UR - https://doi.org/10.1155/2009/941920 DO - 10.1155/2009/941920 JF - International Journal of Mathematics and Mathematical Sciences PB - Hindawi Publishing Corporation KW - ER -