Formal residue and computer-assisted proofs of combinatorial identities

Jin HAITAO

Makale detayları

Formal residue and computer-assisted proofs of combinatorial identities

Yazarlar:

Jin HAITAO

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2018 Vol.42 Issue 5, pp.2466-2480

Belge Tipi:

Makale

Yayın Tarihi:

9/2018

Belge Dili:

Türkçe

Document ID (Org No.):

2000745775

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Özet:

 

The coefficient of x−1x−1x^{-1} of a formal Laurent series f(x)f(x)f(x) is called the formal residue of f(x)f(x)f(x).  Many combinatorial numbers can be represented by the formal residues of hypergeometric terms. With these representations and the extended Zeilberger algorithm, we generate recurrence relations for summations involving combinatorial sequences such as Stirling numbers and their qqq-analog. As examples, we give computer proofs of several known identities and derive some new identities. The applicability of this method is also studied.

Makale detayları

Formal residue and computer-assisted proofs of combinatorial identities

Yazarlar: Jin HAITAO

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2018 Vol.42 Issue 5, pp.2466-2480

Belge Tipi: Makale

Yayın Tarihi: 9/2018

Belge Dili: Türkçe

Document ID (Org No.): 2000745775

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

Jin HAITAO

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2018 Vol.42 Issue 5, pp.2466-2480

Belge Tipi:

Makale

Yayın Tarihi:

9/2018

Belge Dili:

Türkçe

Document ID (Org No.):

2000745775

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098