Finding Euler number using box algebra and generalized skew-hooks (with computer program)
This paper discusses the recursive formula En+1= 1/2EiEn-i, with initial conditions Eo = 1, and E1 = 1, for finding the Euler numbers. These numbers appear as the coefficients of the Maclaurin series expansion for sec x and tan x.The main objective of this paper is to present a nonrecursive formula...
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| Main Authors: | , |
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| 格式: | text |
| 語言: | English |
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Animo Repository
1994
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| 在線閱讀: | https://animorepository.dlsu.edu.ph/etd_bachelors/16156 |
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| 總結: | This paper discusses the recursive formula En+1= 1/2EiEn-i, with initial conditions Eo = 1, and E1 = 1, for finding the Euler numbers. These numbers appear as the coefficients of the Maclaurin series expansion for sec x and tan x.The main objective of this paper is to present a nonrecursive formula for obtaining the Euler numbers. This makes use of skew-hooks and column products. Euler numbers are expressed as linear combinations of multinomial coefficients. Also a computer program was developed to generate some of these Euler numbers. |
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