伴随勒让德多项式（Associated Legendre polynomials，又译缔合勒让德多项式、连带勒让德多项式、关联勒让德多项式）是数学上对如下形式常微分方程解函数串行的称呼：

该方程是在球坐标系下求解拉普拉斯方程时得到的，在数学和理论物理学中有重要的意义。

因上述方程仅当 和 均为整数且满足 时，才在区间 [−1, 1] 上有非奇异解，所以通常把 和 均为整数时方程的解称为伴随勒让德多项式；把 和/或 为一般实数或复数时方程的解称为广义勒让德函数（generalized Legendre functions）。

In mathematics, the associated Legendre polynomials are the canonical solutions of the general Legendre equation

or equivalently

where the indices ℓ and m (which are integers) are referred to as the degree and order of the associated Legendre polynomial respectively. This equation has nonzero solutions that are nonsingular on [−1, 1] only if ℓ and m are integers with 0 ≤ m ≤ ℓ, or with trivially equivalent negative values. When in addition m is even, the function is a polynomial. When m is zero and ℓ integer, these functions are identical to the Legendre polynomials. In general, when ℓ and m are integers, the regular solutions are sometimes called "associated Legendre polynomials", even though they are not polynomials when m is odd. The fully general class of functions with arbitrary real or complex values of ℓ and m are Legendre functions. In that case the parameters are usually labelled with Greek letters.