Counterexamples to Robertson's conjecture

F.W. Steutel

doi:10.1016/0022-247X(91)90258-2

Counterexamples to Robertson's conjecture

F.W. Steutel

Mathematics and Computer Science

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Abstract

We consider the coefficients dnj(y) in {((1 + z)x/(1 - z)x - 1)}y = ¿n=08 zn ¿j = 0n, dnj(y)xj. By use of divisibility results from probability theory it is shown that for every positive, non-integer, rational value of y some of the dnj(y) are negative. For this result yields counterexamples to a conjecture by [4.].

Original language	English
Pages (from-to)	578-582
Number of pages	5
Journal	Journal of Mathematical Analysis and Applications
Volume	158
Issue number	2
DOIs	https://doi.org/10.1016/0022-247X(91)90258-2
Publication status	Published - 1991

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title = "Counterexamples to Robertson's conjecture",

abstract = "We consider the coefficients dnj(y) in {((1 + z)x/(1 - z)x - 1)}y = ¿n=08 zn ¿j = 0n, dnj(y)xj. By use of divisibility results from probability theory it is shown that for every positive, non-integer, rational value of y some of the dnj(y) are negative. For this result yields counterexamples to a conjecture by [4.].",

author = "F.W. Steutel",

year = "1991",

doi = "10.1016/0022-247X(91)90258-2",

language = "English",

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pages = "578--582",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "2",

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T1 - Counterexamples to Robertson's conjecture

AU - Steutel, F.W.

PY - 1991

Y1 - 1991

N2 - We consider the coefficients dnj(y) in {((1 + z)x/(1 - z)x - 1)}y = ¿n=08 zn ¿j = 0n, dnj(y)xj. By use of divisibility results from probability theory it is shown that for every positive, non-integer, rational value of y some of the dnj(y) are negative. For this result yields counterexamples to a conjecture by [4.].

AB - We consider the coefficients dnj(y) in {((1 + z)x/(1 - z)x - 1)}y = ¿n=08 zn ¿j = 0n, dnj(y)xj. By use of divisibility results from probability theory it is shown that for every positive, non-integer, rational value of y some of the dnj(y) are negative. For this result yields counterexamples to a conjecture by [4.].

U2 - 10.1016/0022-247X(91)90258-2

DO - 10.1016/0022-247X(91)90258-2

M3 - Article

SN - 0022-247X

VL - 158

SP - 578

EP - 582

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Counterexamples to Robertson's conjecture

Abstract

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