Results 241 to 250 of about 101,104 (278)

Identities for Bernoulli polynomials and Bernoulli numbers

Archiv der Mathematik, 2014
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Alzer, Horst, Kwong, Man Kam
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Bernoulli Polynomials and Bernoulli Numbers

1973
The 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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Generalized Bernoulli-Hurwitz numbers and the universal Bernoulli numbers

Russian Mathematical Surveys, 2011
The three fundamental properties of the Bernoulli numbers, namely, the von Staudt-Clausen theorem, von Staudt's second theorem, and Kummer's original congruence, are generalized to new numbers that we call generalized Bernoulli-Hurwitz numbers. These are coefficients in the power series expansion of a higher-genus algebraic function with respect to a ...
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Generalized Bernoulli Numbers

2014
In this chapter we introduce generalized Bernoulli numbers and Bernoulli polynomials. Generalized Bernoulli numbers are Bernoulli numbers twisted by a Dirichlet character, which we define at the beginning of the first section. Bernoulli polynomials are generalizations of Bernoulli numbers with an indeterminate.
Tomoyoshi Ibukiyama, Masanobu Kaneko
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q-Bernoulli and Eulerian Numbers

Transactions of the American Mathematical Society, 1954
In einer früheren Arbeit [Duke Math. J. 15, 987--1000 (1948; Zbl 0032.00304)] definierte der Verf. die rationalen Funktionen \(\eta_m\) der Unbestimmten \(q\) durch die symbolischen Formeln (in welchen nach der Entwicklung \(\eta^m\) durch \(\eta_m\) ersetzt wird) \((q\eta+1)^m=\eta^m\) \((m>1)\), \(\eta_0=1\), \(\eta_1=0\) und die polynome \(\eta_m(x)\
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Stirling Numbers and Bernoulli Numbers

2014
In this chapter we give a formula that describes Bernoulli numbers in terms of Stirling numbers. This formula will be used to prove a theorem of Clausen and von Staudt in the next chapter. As an application of this formula, we also introduce an interesting algorithm to compute Bernoulli numbers.
Tomoyoshi Ibukiyama, Masanobu Kaneko
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Bernoulli Numbers

1982
Kenneth Ireland, Michael Rosen
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Bernoulli Numbers

2014
Tomoyoshi Ibukiyama, Masanobu Kaneko
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The Labeled Multi-Bernoulli Filter

IEEE Transactions on Signal Processing, 2014
Ba-Tuong Vo, Stephan Reuter, Ba-Ngu Vo
exaly  

An isogeometric collocation approach for Bernoulli–Euler beams and Kirchhoff plates

Computer Methods in Applied Mechanics and Engineering, 2015
Alessandro Reali, Hector Gomez
exaly