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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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.].

Originele taal-2	Engels
Pagina's (van-tot)	578-582
Aantal pagina's	5
Tijdschrift	Journal of Mathematical Analysis and Applications
Volume	158
Nummer van het tijdschrift	2
DOI's	https://doi.org/10.1016/0022-247X(91)90258-2
Status	Gepubliceerd - 1991

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

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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.].",

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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.].

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Counterexamples to Robertson's conjecture

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