Rational combinations for the sums involving inverse binomial coefficients

Gi Sang Cheon; Toufik Mansour

doi:10.1016/j.amc.2011.08.003

Rational combinations for the sums involving inverse binomial coefficients

Gi Sang Cheon, Toufik Mansour

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We say that the number r can be expressed as a rational combination of the set T = {f_i|i ∈ I} if there exist rational numbers d_i such that r=∑_i∈Id_if_i. In this paper, we study rational combinations for sums involving inverse binomial coefficients of the form: ∑_n≥0n(pn+k qn)^-1xⁿ, (x∈ℚ) where p,q,k∈ℕ₀ and {a_n} is any rational sequence. In several interesting cases of the sum, we obtain closed forms, recursion formulas and experimental results.

Original language	English
Pages (from-to)	2641-2646
Number of pages	6
Journal	Applied Mathematics and Computation
Volume	218
Issue number	6
DOIs	https://doi.org/10.1016/j.amc.2011.08.003
State	Published - 15 Nov 2011

Keywords

Beta function
Binomial coefficient
Rational combination

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

Access to Document

10.1016/j.amc.2011.08.003

Cite this

@article{738398aea1884dc9ba34412cfd8574b2,

title = "Rational combinations for the sums involving inverse binomial coefficients",

abstract = "We say that the number r can be expressed as a rational combination of the set T = {fi|i ∈ I} if there exist rational numbers di such that r=∑i∈Idifi. In this paper, we study rational combinations for sums involving inverse binomial coefficients of the form: ∑n≥0n(pn+k qn)-1xn, (x∈ℚ) where p,q,k∈ℕ0 and {an} is any rational sequence. In several interesting cases of the sum, we obtain closed forms, recursion formulas and experimental results.",

keywords = "Beta function, Binomial coefficient, Rational combination",

author = "Cheon, {Gi Sang} and Toufik Mansour",

year = "2011",

month = nov,

day = "15",

doi = "10.1016/j.amc.2011.08.003",

language = "English",

volume = "218",

pages = "2641--2646",

journal = "Applied Mathematics and Computation",

issn = "0096-3003",

publisher = "Elsevier",

number = "6",

}

TY - JOUR

T1 - Rational combinations for the sums involving inverse binomial coefficients

AU - Cheon, Gi Sang

AU - Mansour, Toufik

PY - 2011/11/15

Y1 - 2011/11/15

N2 - We say that the number r can be expressed as a rational combination of the set T = {fi|i ∈ I} if there exist rational numbers di such that r=∑i∈Idifi. In this paper, we study rational combinations for sums involving inverse binomial coefficients of the form: ∑n≥0n(pn+k qn)-1xn, (x∈ℚ) where p,q,k∈ℕ0 and {an} is any rational sequence. In several interesting cases of the sum, we obtain closed forms, recursion formulas and experimental results.

AB - We say that the number r can be expressed as a rational combination of the set T = {fi|i ∈ I} if there exist rational numbers di such that r=∑i∈Idifi. In this paper, we study rational combinations for sums involving inverse binomial coefficients of the form: ∑n≥0n(pn+k qn)-1xn, (x∈ℚ) where p,q,k∈ℕ0 and {an} is any rational sequence. In several interesting cases of the sum, we obtain closed forms, recursion formulas and experimental results.

KW - Beta function

KW - Binomial coefficient

KW - Rational combination

UR - http://www.scopus.com/inward/record.url?scp=80053284823&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2011.08.003

DO - 10.1016/j.amc.2011.08.003

M3 - Article

AN - SCOPUS:80053284823

SN - 0096-3003

VL - 218

SP - 2641

EP - 2646

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 6

ER -

Rational combinations for the sums involving inverse binomial coefficients

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this