Abel–rothe Type Generalizations of Jacobi’s Triple Product Identity
نویسنده
چکیده
Abstract. Using a simple classical method we derive bilateral series identities from terminating ones. In particular, we show how to deduce Ramanujan’s 1ψ1 summation from the q-Pfaff–Saalschütz summation. Further, we apply the same method to our previous q-Abel–Rothe summation to obtain, for the first time, Abel–Rothe type generalizations of Jacobi’s triple product identity. We also give some results for multiple series.
منابع مشابه
Touchard-Riordan formulas, T -fractions, and Jacobi’s triple product identity
Abstract. We give a combinatorial proof of a Touchard-Riordan-like formula discovered by the first author. As a consequence we find a connection between his formula and Jacobi’s triple product identity. We then give a combinatorial analog of Jacobi’s triple product identity by showing that a finite sum can be interpreted as a generating function of weighted Schröder paths, so that the triple pr...
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