  In the theory of the Nil-DAHA Fourier transform, the inner products of
q-Hermite polynomials for the measure function multiplied by a level one theta
function are the key. They are used to obtain expansions of products of any
number of such theta functions in terms of the q-Hermite polynomials. An ample
family of modular functions satisfying Rogers-Ramanujan type identities for
arbitrary (reduced, twisted) affine root systems is obtained as an application.
A relation to Rogers dilogarithm and Nahm's conjecture is discussed. Some of
our q-series can be identified with known ones, but their interpretation seems
new. Using that the q-Hermite polynomials are closely related to the Demazure
level one characters in the twisted case (Sanderson, Ion), we outline a
connection of our formulas to the level one integrable Kac-Moody modules and
the coset theory. Several instances of the level-rank duality are provided.
