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Some further results on Legendre numbers

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  • Paul W. Haggard

Abstract

The Legendre numbers, P n m , are expressed in terms of those numbers, P k m − 1 , in the previous column down to P n m and in terms of those, P k m , 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.

Suggested Citation

  • Paul W. Haggard, 1988. "Some further results on Legendre numbers," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 11, pages 1-5, January.
    • Handle: RePEc:hin:jijmms:945974
    DOI: 10.1155/S0161171288000754
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