多重对数函数（英语：polylogarithm，也称：Jonquière's function）是数学中一种特殊的幂级数，定义为：

一般来说，多重对数函数不像对数函数那样是一个初等函数。上述定义中，自变量|z| < 1，s对所有复数值有效。通过解析延拓，可以将z的定义域扩展到更大的范围。

s = 1时的多重对数函数可以用自然对数表示（Li₁(z) = −ln(1−z)），s = 2和3的多重对数函数分别称为dilogarithm及trilogarithm，其名称的由来是多重对数函数表示为以下的递归积分式：

In mathematics, the polylogarithm (also known as Jonquière's function, for Alfred Jonquière) is a special function Li_s(z) of order s and argument z. Only for special values of s does the polylogarithm reduce to an elementary function such as the natural logarithm or rational functions. In quantum statistics, the polylogarithm function appears as the closed form of integrals of the Fermi–Dirac distribution and the Bose–Einstein distribution, and is also known as the Fermi–Dirac integral or the Bose–Einstein integral. In quantum electrodynamics, polylogarithms of positive integer order arise in the calculation of processes represented by higher-order Feynman diagrams.