Table of associated Legendre functions of the second kind for values on the real axis

This dataset is a tabulation of associated Legendre functions of the second, sometimes called the irregular solutions, computed for values on the real axis ranging from 0.0 to 10.0. It was created by a new program which has been implemented in C++ using template meta programming, to compute associated Legendre functions of the first and second kind of integer order (l) and degree (m) and complex argument (z). The mathematical equations, along with a short table of values, are given the book (see page 118 and following) Shanjie Zhang and Jianming Jin, Computation of Special Functions,<br> publishers: Wiley, 1996, ISBN: 0-471-11963-6,<br> LC: QA351.C45. The output from this new program has been verified against the tables printed in the book. This dataset is provided because i) it covers a wider range of arguments than published in the tables in the book ii) it has many more l,m values than the tables in the book Note that this data set was computed using data type long double on an Intel CPU.本数据集为第二类连带勒让德函数（Associated Legendre functions of the second kind，又称非正则解）的数值制表结果，计算覆盖实轴上0.0至10.0的取值区间。该数据集由一款采用C++语言实现模板元编程（Template Meta Programming）的全新程序生成，可计算整数阶数(l)、次数(m)及复自变量(z)下的第一类与第二类连带勒让德函数。相关数学公式与简短数值表见于专著《特殊函数计算》（Computation of Special Functions，作者张善杰、金建明，Wiley出版社1996年出版，ISBN：0-471-11963-6，LC分类号：QA351.C45），具体内容请参见第118页及后续章节。本程序的输出结果已与该专著刊载的数值表完成验证比对。推出本数据集的缘由有二：其一，其覆盖的自变量范围较原书表格更广；其二，其包含的(l,m)参数组合数量远多于原书表格。需注意，本数据集是在Intel CPU上采用long double数据类型计算得到的。