Andrews and El Bachraoui prove a two-variable generalization of the Hecke sum identity for S(q) via Bailey pairs, recovering the even and odd cases as corollaries when a=1.
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Solutions for Hecke Sum Questions of Banerjee and Bringmann
Andrews and El Bachraoui prove a two-variable generalization of the Hecke sum identity for S(q) via Bailey pairs, recovering the even and odd cases as corollaries when a=1.