We consider Carlitz -Bernoulli numbers and -Stirling numbers of the first and the second kinds. From the properties of -Stirling numbers, we derive many interesting formulas associated with Carlitz -Bernoulli numbers. Finally, we will prove where
Kim Taekyun
doaj
We define the twisted -Bernoulli polynomials and the twisted generalized -Bernoulli polynomials attached to of higher order and investigate some symmetric properties of them.
Lee B +5 more
doaj
On Generations of the Numbers of Bernoulli and Euler [PDF]
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Jennings-Shaffer C +3 more
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Salim I, Okasha N, Barbary M, Anis W.
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On a Bernoulli numbers conjectures.
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