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A Series Solution to the Luminosity Distance in a Flat LCDM Universe

Cosmological observations indicate that our universe is flat and dark energy (DE) dominated at present. The luminosity distance plays an important role in the investigation of the evolution and structure of the universe. Nevertheless, the evaluation of the luminosity distance d_L is associated computationally heavy numerical quadratures in practice. In this Letter we find a series solution of the luminosity distance in a spatially flat LCDM cosmological model. And it is further shown that the series solution has a relative error of less than 0.36% for any relative parameter β(β= Omega_m / Omega_L) from zero to four, i.e. 0.2 < Omega_L < 1 and redshift z > 0.1 when the order of the series is n = 100.