We investigate a novel symmetry in dualities of Wu's equation: #omega#~g(1 + #omega#)~(1 - g) = e~(#beta#(#epsilon# - #mu#) for a degenerate g-on gas with fractional exclusion statistics of g, where #beta# = 1/#kappa#_BT, implied the energy, and #mu# the chemical potential of the system. We find that the particle-hole duality between g and 1/g and the supersymmetric duality between g and 1 - g form a novel quasi-modular group of order six for Wu's equation. And we show that many physical quantities in quantum systems with the fractional exclusion statistics can be represented in terms of quasi-hypergeometric functions and that the quasi-modular symmetry acts on these functions.
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