Open AccessOn Legendre numbers of the second kind
Author(s) -
Paul W. Haggard
Publication year - 1988
Publication title -
international journal of mathematics and mathematical sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 39
eISSN - 1687-0425
pISSN - 0161-1712
DOI - 10.1155/s0161171288000997
Subject(s) - legendre polynomials , legendre function , legendre's equation , mathematics , legendre transformation , associated legendre polynomials , table (database) , series (stratigraphy) , combinatorics , mathematical analysis , computer science , classical orthogonal polynomials , paleontology , gegenbauer polynomials , biology , orthogonal polynomials , data mining
The Legendre numbers of the second kind, an infinite set of rational numbers, are defined from the associated Legendre functions. An explicit formula and a partial table for these numbers are given and many elementary properties are presented. A connection is shown between Legendre numbers of the first and second kinds. Extended Legendre numbers of the first and second kind are defined in a natural way and these are expressed in terms of those of the second and first kind, respectively. Two other sets of rational numbers are defined from the associated Legendre functions by taking derivatives and evaluating these at x=0. One of these sets is connected to Legendre numbers of the first find while the other is connected to Legendre numbers of the second kind. Some series are also discussed