  We show that the generalized Bernstein bases in Muntz spaces defined by
Hirschman and Widder [7] and extended by Gelfond [6] can be obtained as limits
of the Chebyshev-Bernstein bases in Muntz spaces with respect to an interval
[a,1] as the real number, a, converges to zero. Such a realization allows for
concepts of curve design such as de Casteljau algorithm, blossom, dimension
elevation to be translated from the general theory of Chebyshev blossom in
Muntz spaces to these generalized Bernstein bases that we termed here as
Gelfond-Bernstein bases. The advantage of working with Gelfond-Bernstein bases
lies in the simplicity of the obtained concepts and algorithms as compared to
their Chebyshev-Bernstein bases counterparts.
