After proving the Khintchine inequality for the n-Rademacher functions of ARON and GLOBVENIK With constants independent from n is an element of N, applications are given to the theory of polynomials and holomorphic functions between Banach spaces. In particular, the following result is proved: Every entire mapping from a Banach space into another one of cotype q, vanishing at the origin and of r-dominated type at zero for some r > 0 maps unconditionally 2-summable sequences into absolutely q-summable sequences.1766572