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Enhancing wellbore stability through machine learning for sustainable hydrocarbon exploitation. [PDF]
Sci RepMahetaji M, Brahma J.
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The Fibonacci Quarterly, 1968
This paper is of an expository nature and is concerned mainly with the arithmetic properties of the Bernoulli numbers. Following an introductory section which reviews the basic formulas for the Bernoulli and Euler numbers and polynomials, the following topics are discussed: the Staudt-Clausen theorem, Kummer's congruences and some related properties ...
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This paper is of an expository nature and is concerned mainly with the arithmetic properties of the Bernoulli numbers. Following an introductory section which reviews the basic formulas for the Bernoulli and Euler numbers and polynomials, the following topics are discussed: the Staudt-Clausen theorem, Kummer's congruences and some related properties ...
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Bernoulli Polynomials and Bernoulli Numbers
2002In this chapter, we introduce a sequence of polynomials that is closely related to the h-antiderivative of polynomials and has many important applications.
Victor Kac, Pokman Cheung
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Identities for Bernoulli polynomials and Bernoulli numbers
Archiv der Mathematik, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alzer, Horst, Kwong, Man Kam
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Bernoulli Polynomials and Bernoulli Numbers
1973The summing of the first n natural numbers, or Squares, or cubes, is a rather elementary problem in number theory and leads to the well known formulae $$\eqalign{ & \sum\limits_{n = 1}^N n \, = \,{{N(N + 1)} \over 2}, \cr & \sum\limits_{n = 1}^N {{n^2}} \, = \,{{N(N + 1)(2N + 1)} \over 6}, \cr & \sum\limits_{n = 1}^N {{n^3}} \, = \,{{{N^2}{{(N + 1)}
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