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 dLis associated computationally heavy numerical quadratures in practice.In this Letter we find a series solution of the luminosity distance in a spatially flatΛCDM 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≡ Ωm Ω Λ form zero to four,i.e.0.2Ω Λ 1and redshift z0.1when the order of the series in n=100.%宇宙学观测表明,目前宇宙的时空结构为平坦的且以暗能量（DE）为主要成分.光度距离对于研究宇宙的结构和演化具有重要意义,然而它在实际应用时需要进行繁重的数值求积过程.本文得到一个平坦ΛCDM宇宙学模型下的光度距离级数解.经过计算发现,在多项式阶数n=100,相对参数β∈[0,4]（即0.2〈ΩΛ〈1,红移z〉0.1）时,其相对误差低于0.36%.
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