Turán type inequalities for the partial sums of the generating functions of Bernoulli and Euler numbers

Turán type inequalities for the partial sums of the generating functions of the Bernoulli and Euler numbers are established. They are shown to follow from a general result relating Turán inequalities of partial sums with Turán inequalities of the corresponding remainders in any Maclaurin expansion....

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Veröffentlicht in:	Mathematische Nachrichten 2012-12, Vol.285 (17-18), p.2129-2156
Hauptverfasser:	Koumandos, Stamatis, Pedersen, Henrik Laurberg
Format:	Artikel
Sprache:	eng
Schlagworte:	26D07 26D15 33E20 41A60 41A80 Bernoulli numbers completely monotonic functions of positive order Euler numbers generating functions MSC Primary: 11B68 ratio of series of functions remainders in asymptotic expansions Secondary: 11B83 Turán inequality β-function
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