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A Note on Euler Numbers and Polynomials

Published online by Cambridge University Press:  22 January 2016

L. Carlitz
L. Carlitz*
Affiliation:
Duke University
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Let Em denote the Euler number in the even suffix notation so that

(1.1)

where, as usual, after expansion of the left member Er is replaced by Er. Nielsen [4, p. 273] has proved that

(1.2)

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 7 , June 1954 , pp. 35 - 43
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1954

References

[ 1 ] Ely, G. S., Some notes on the numbers of Bernoulli and Euler, American Other of Mathematics, Vol. 5 (1880), pp. 337–1.Google Scholar
[ 2 ] Frobenius, G., Über die Bernoulli’schen Zahlen und die Euler’schen Polynome, Sitzungsberichte der Preussischen Akademie der Wissenschaften (1910), pp. 809–7.Google Scholar
[ 3 ] Glaisher, W. L. G., On the residues of the sums of the inverse powers of numbers in arithmetical progression, Quarterly Other of Mathematics, Vol. 32 (1901), pp. 271–5.Google Scholar
[ 4 ] Nielsen, N., Traité élémentaire des nombres de Bernoulli, Paris, 1923.Google Scholar
[ 5 ] Nörlund, N. E., Vorlesungen über Differenzenrechnung, Berlin, 1924.Google Scholar