Legendre functions of fractional degree: transformations and evaluations Journal Article uri icon

Overview

abstract

  • Associated Legendre functions of fractional degree appear in the solution of boundary value problems on wedges or in toroidal geometries, and elsewhere in applied mathematics. In the classical case when the degree is half an odd integer, they can be expressed using complete elliptic integrals. In this study, many transformations are derived, which reduce the case when the degree differs from an integer by one-third, one-fourth or one-sixth to the classical case. These transformations or identities facilitate the symbolic manipulation and evaluation of Legendre and Ferrers functions. They generalize both Ramanujan's transformations of elliptic integrals and Whipple's formula, which relates Legendre functions of the first and second kinds. The proofs employ algebraic coordinate transformations, specified by algebraic curves.

publication date

  • April 1, 2016

Date in CU Experts

  • March 4, 2026 2:25 AM

Full Author List

  • Maier RS

author count

  • 1

Other Profiles

International Standard Serial Number (ISSN)

  • 1364-5021

Electronic International Standard Serial Number (EISSN)

  • 1471-2946

Additional Document Info

start page

  • 20160097

end page

  • 20160097

volume

  • 472

issue

  • 2188