Some further results on Legendre numbers

[摘要] The Legendre numbers,Pnm, are expressed in terms of those numbers,Pkm−1, in the previous column down toPnmand in terms of those,Pkm, above but in the same column. Other results are given for numbers close to a given number. The limit of the quotient of two consecutive non-zero numbers in any one column is shown to be−1. Bounds for the Legendre numbers are described by circles centered at the origin. A connection between Legendre numbers and Pascal numbers is exhibited by expressing the Legendre numbers in terms of combinations.

[学科分类] 数学（综合）