Some further results on Legendre numbers
The Legendre numbers, Pnm, are expressed in terms of those numbers, Pkm−1, in the previous column down to Pnm and 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 on...
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| Format: | Article |
| Language: | English |
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Wiley
1988-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171288000754 |
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| _version_ | 1832558991698296832 |
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| author | Paul W. Haggard |
| author_facet | Paul W. Haggard |
| author_sort | Paul W. Haggard |
| collection | DOAJ |
| description | The Legendre numbers, Pnm, are expressed in terms of those numbers, Pkm−1, in the previous column down to Pnm and 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. |
| format | Article |
| id | doaj-art-44e4d3c962d746d2b2c2eef296e3dd0f |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1988-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-44e4d3c962d746d2b2c2eef296e3dd0f2025-02-03T01:31:09ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251988-01-0111361962310.1155/S0161171288000754Some further results on Legendre numbersPaul W. Haggard0Department of Mathematics, Last Carolina University, Greenville 27858, North Carolina, USAThe Legendre numbers, Pnm, are expressed in terms of those numbers, Pkm−1, in the previous column down to Pnm and 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.http://dx.doi.org/10.1155/S0161171288000754associated Legendre functionsbounds for the Legendre numbersLegendre numbersLegendre polynomialslimits of ratios of Legendre numbers. |
| spellingShingle | Paul W. Haggard Some further results on Legendre numbers International Journal of Mathematics and Mathematical Sciences associated Legendre functions bounds for the Legendre numbers Legendre numbers Legendre polynomials limits of ratios of Legendre numbers. |
| title | Some further results on Legendre numbers |
| title_full | Some further results on Legendre numbers |
| title_fullStr | Some further results on Legendre numbers |
| title_full_unstemmed | Some further results on Legendre numbers |
| title_short | Some further results on Legendre numbers |
| title_sort | some further results on legendre numbers |
| topic | associated Legendre functions bounds for the Legendre numbers Legendre numbers Legendre polynomials limits of ratios of Legendre numbers. |
| url | http://dx.doi.org/10.1155/S0161171288000754 |
| work_keys_str_mv | AT paulwhaggard somefurtherresultsonlegendrenumbers |