Journal of the Ramanujan Mathematical Society
Volume 39, Issue 2, June 2024 pp. 187–192.
On a generalization of vanishing coefficients in two q-series expansions
Authors:
Channabasavayya and Ranganatha Dasappa
Author institution:Department of Mathematics, Central University of Karnataka,
Kalaburagi~585~367, Karnataka, India.
Summary:
If the sequences {g(n)} and {h(n)} are defined by
⅀{n={-∞}}{∞}g(n)q{n} = {(q{2t},
q{5-2t};q{5})}{∞}{(± q{5-t},± q{5+t};
q{10})}{∞}{2},
⅀{n={-∞}}{∞}h(n)q{n}={(± q{2t},
± q{5-2t};q{5})}{∞}{2}{(q{2t},q{10-2t};q{10})}{∞},
then we prove that g(5n+t)=h(5n+3t{2}-2t)=0, where t≥ 1 and 5 ⫮ t.
These vanishing coefficient results generalize the results of Tang,
Somashekara and Thulasi, Tang and Xia, and, Dou and Xiao.
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