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Approximation of analytic functions of exponential derived and integral bases in Fréchet spaces

The purpose of this paper is to establish some theorems on the representation of analytic functions by exponential derived bases and exponential integral bases in Fréchet spaces. Theorems are proven to show such that representation is possible in closed disks, open disks, open regions surrounding closed disks, at the origin and for all entire functions. Also, some results concerning the growth order and type of EDBs and EIBs are determined. Moreover, the -property of and are discussed. Finally, some applications to the and of Bernoulli, Euler, Bessel, and Chebyshev polynomials have been studied.