  We first show that hypergeometric functions appear naturally as spectral
functions when applying pseudo-differential calculus to decipher heat kernel
asymptotic in the situation where the symbol algebra is noncommutative. Such
observation leads to a unified (works for arbitrary dimension) method of
computing the modular curvature on toric noncommutative manifolds. We show that
the spectral functions that define the quantum part of the curvature have
closed forms in terms of hypergeometric functions. As a consequence, we are
able to obtained explicit expressions (as functions in the dimension parameter)
for those spectral functions without using symbolic integration. A surprising
geometric consequence is that the functional relations coming from the
variation of the associated Einstein-Hilbert action still hold when the
dimension parameter takes real values.
