The ratio between the tail of a series and its approximating integral.

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The ratio between the tail of a series and its approximating integral. / Jameson, Graham J. O.
In: Journal of Inequalities in Pure and Applied Mathematics, Vol. 4, No. 2, 01.04.2003, p. 1-12.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Jameson, Graham J. O. / The ratio between the tail of a series and its approximating integral. In: Journal of Inequalities in Pure and Applied Mathematics. 2003 ; Vol. 4, No. 2. pp. 1-12.

Bibtex

@article{d7c4bccb470845d1880cee2629277773,

title = "The ratio between the tail of a series and its approximating integral.",

abstract = "For a strictly positive function , let and , assumed convergent. If is increasing, then is decreasing and is increasing. If is increasing, then is decreasing. Under suitable conditions, analogous results are obtained for the ``continuous tail'' defined by : these results apply, in particular, to the Hurwitz zeta function.",

author = "Jameson, {Graham J. O.}",

year = "2003",

month = apr,

day = "1",

language = "English",

volume = "4",

pages = "1--12",

journal = "Journal of Inequalities in Pure and Applied Mathematics",

issn = "1443-5756",

publisher = "Victoria University of Technology",

number = "2",

}

RIS

TY - JOUR

T1 - The ratio between the tail of a series and its approximating integral.

AU - Jameson, Graham J. O.

PY - 2003/4/1

Y1 - 2003/4/1

N2 - For a strictly positive function , let and , assumed convergent. If is increasing, then is decreasing and is increasing. If is increasing, then is decreasing. Under suitable conditions, analogous results are obtained for the ``continuous tail'' defined by : these results apply, in particular, to the Hurwitz zeta function.

AB - For a strictly positive function , let and , assumed convergent. If is increasing, then is decreasing and is increasing. If is increasing, then is decreasing. Under suitable conditions, analogous results are obtained for the ``continuous tail'' defined by : these results apply, in particular, to the Hurwitz zeta function.

M3 - Journal article

VL - 4

SP - 1

EP - 12

JO - Journal of Inequalities in Pure and Applied Mathematics

JF - Journal of Inequalities in Pure and Applied Mathematics

SN - 1443-5756

IS - 2

ER -

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