论文标题
Francesco Carlini：开普勒方程和渐近方程的渐近解决方案
Francesco Carlini: Kepler's equation and the asymptotic solution to singular differential equations
论文作者
论文摘要
Carlini的职业生涯主要致力于天文学，但他还是一位特别熟练的数学家。在本文中，我们将详细收集和分析他的数学贡献。特别是，在他1817年的重要回忆录中，他介绍了开普勒方程式，他引入了一种创新的想法，通过渐近扩张来解决具有单一扰动的普通微分方程。在拉普拉斯（Laplace）的贡献之前五年中，也出现了同一回忆录中，通常称为拉普拉斯极限常数。此外，卡利尼（Carlini）提前70年发表了其他数学回忆录，这是兰伯特（Lambert）特殊功能的复杂分支的重要性。
Carlini's career was mainly dedicated to astronomy, but he was also a particularly skilled mathematician. In this article we collect and analyse his mathematical contributions in detail. In particular, in his important Memoir of the year 1817 devoted to Kepler's equation he introduced an innovative idea to solve ordinary differential equations with singular perturbations by means of asymptotic expansions. In the same Memoir also appeared, five years before Laplace's contributions, what is usually called the Laplace limit constant. Furthermore, Carlini published other mathematical Memoirs anticipating, 70 years in advance, the importance of complex branches of the Lambert's special function.
