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Turán type inequalities for the partial sums of the generating functions of Bernoulli and Euler numbers
Author(s) -
Koumandos Stamatis,
Pedersen Henrik Laurberg
Publication year - 2012
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201100299
Subject(s) - mathematics , bernoulli number , euler's formula , bernoulli's principle , monotonic function , type (biology) , inequality , order (exchange) , function (biology) , pure mathematics , mathematical analysis , ecology , engineering , biology , aerospace engineering , finance , evolutionary biology , economics
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. Remainders in asymptotic expansions of the β‐function are shown to be completely monotonic of positive order.