A RECIPROCITY THEOREM FOR CERTAIN q-SERIES FOUND IN RAMANUJAN’S LOST NOTEBOOK
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چکیده
Three proofs are given for a reciprocity theorem for a certain q-series found 7 in Ramanujan’s lost notebook. The first proof uses Ramanujan’s 1ψ1 summation the8 orem, the second employs an identity of N. J. Fine, and the third is combinatorial. 9 Next, we show that the reciprocity theorem leads to a two variable generalization of 10 the quintuple product identity. The paper concludes with an application to sums of 11 three squares. 12
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تاریخ انتشار 2003