“Trinomial expansion”的意思、由来-开放百科全书

词条

Trinomial expansion

释义

See also
References

In mathematics, a trinomial expansion is the expansion of a power of a sum of three terms into monomials. The expansion is given by

where {{math|n}} is a nonnegative integer and the sum is taken over all combinations of nonnegative indices {{math|i, j,}} and {{math|k}} such that {{math|i + j + k {{=}} n}}.^[1] The trinomial coefficients are given by

This formula is a special case of the multinomial formula for {{math|m {{=}} 3}}. The coefficients can be defined with a generalization of Pascal's triangle to three dimensions, called Pascal's pyramid or Pascal's tetrahedron.^[2]

The number of terms of an expanded trinomial is the triangular number

where {{math|n}} is the exponent to which the trinomial is raised.^[3]

References

1. ^{{citation|title=Discrete Mathematics with Applications|first=Thomas|last=Koshy|publisher=Academic Press|year=2004|isbn=9780080477343|url=https://books.google.com/books?id=90KApidK5NwC&pg=PA889|page=889}}.
2. ^{{citation|title=Combinatorics and Graph Theory|series=Undergraduate Texts in Mathematics|first1=John|last1=Harris|first2=Jeffry L.|last2=Hirst|first3=Michael|last3=Mossinghoff|edition=2nd|publisher=Springer|year=2009|isbn=9780387797113|page=146|url=https://books.google.com/books?id=DfcQaZKUVLwC&pg=PA146}}.
3. ^{{citation|last=Rosenthal|first=E. R.|title=A Pascal pyramid for trinomial coefficients|journal=The Mathematics Teacher|year=1961|volume=54|issue=5|pages=336–338}}.

1 : Factorial and binomial topics

随便看

开放百科全书收录14589846条英语、德语、日语等多语种百科知识，基本涵盖了大多数领域的百科知识，是一部内容自由、开放的电子版国际百科全书。

See also

References