Published November 28, 2019 | Version 1.0

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

Authors/Creators

  • 1. Queen's University Belfast

Description

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,
     publishers: Wiley, 1996, ISBN: 0-471-11963-6,
     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. 

 

Files

Files (2.4 MB)

Additional details

Funding

European Commission
ALLScale - An Exascale Programming, Multi-objective Optimisation and Resilience Management Environment Based on Nested Recursive Parallelism 671603