Euler Basis, Identities, and Their Applications

D. S. Kim and T. Kim

International Journal of Mathematics and Mathematical Sciences, 2012, vol. 2012, 1-15

Abstract:

Let 𠑉 ð ‘› = { ð ‘ ( ð ‘¥ ) ∈ â„š [ ð ‘¥ ] | d e g ð ‘ ( ð ‘¥ ) ≤ ð ‘› } be the ( ð ‘› + 1 ) -dimensional vector space over â„š . We show that { ð ¸ 0 ( ð ‘¥ ) , ð ¸ 1 ( ð ‘¥ ) , … , ð ¸ ð ‘› ( ð ‘¥ ) } is a good basis for the space 𠑉 ð ‘› , for our purpose of arithmetical and combinatorial applications. Thus, if ð ‘ ( ð ‘¥ ) ∈ â„š [ ð ‘¥ ] is of degree ð ‘› , then ∑ ð ‘ ( ð ‘¥ ) = ð ‘› ð ‘™ = 0 ð ‘ ð ‘™ ð ¸ ð ‘™ ( ð ‘¥ ) for some uniquely determined ð ‘ ð ‘™ ∈ â„š . In this paper we develop method for computing ð ‘ ð ‘™ from the information of ð ‘ ( ð ‘¥ ) .

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:343981

DOI: 10.1155/2012/343981

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