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  2. Bernoulli number - Wikipedia

    en.wikipedia.org/wiki/Bernoulli_number

    In mathematics, the Bernoulli numbers B n are a sequence of rational numbers which occur frequently in analysis.The Bernoulli numbers appear in (and can be defined by) the Taylor series expansions of the tangent and hyperbolic tangent functions, in Faulhaber's formula for the sum of m-th powers of the first n positive integers, in the Euler–Maclaurin formula, and in expressions for certain ...

  3. Gregory coefficients - Wikipedia

    en.wikipedia.org/wiki/Gregory_coefficients

    Download as PDF; Printable version; ... also known as reciprocal logarithmic numbers, Bernoulli numbers of the second kind, or Cauchy numbers of the first kind, [1 ...

  4. Kummer's congruence - Wikipedia

    en.wikipedia.org/wiki/Kummer's_congruence

    The simplest form of Kummer's congruence states that ()where p is a prime, h and k are positive even integers not divisible by p−1 and the numbers B h are Bernoulli numbers.

  5. Talk:Bernoulli number - Wikipedia

    en.wikipedia.org/wiki/Talk:Bernoulli_number

    The following removed paragraphs are personal opinions of Peter Luschny, see an essay of Luschny The Bernoulli Confusion. This guy (is he an expert on number theory or a graduate mathematician at all? I don't think so!) rigidly claims, against the consensus of experts, to change the definition of Bernoulli numbers so that B(1) = 1/2.

  6. Von Staudt–Clausen theorem - Wikipedia

    en.wikipedia.org/wiki/Von_Staudt–Clausen_theorem

    In number theory, the von Staudt–Clausen theorem is a result determining the fractional part of Bernoulli numbers, found independently by Karl von Staudt and Thomas Clausen . Specifically, if n is a positive integer and we add 1/ p to the Bernoulli number B 2 n for every prime p such that p − 1 divides 2 n , then we obtain an integer; that is,

  7. Ars Conjectandi - Wikipedia

    en.wikipedia.org/wiki/Ars_Conjectandi

    The cover page of Ars Conjectandi. Ars Conjectandi (Latin for "The Art of Conjecturing") is a book on combinatorics and mathematical probability written by Jacob Bernoulli and published in 1713, eight years after his death, by his nephew, Niklaus Bernoulli.

  8. Bernoulli numbers - Wikipedia

    en.wikipedia.org/?title=Bernoulli_numbers&...

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  9. Particular values of the Riemann zeta function - Wikipedia

    en.wikipedia.org/wiki/Particular_values_of_the...

    The zeta function values listed below include function values at the negative even numbers (s = −2, −4, etc.), for which ζ(s) = 0 and which make up the so-called trivial zeros. The Riemann zeta function article includes a colour plot illustrating how the function varies over a continuous rectangular region of the complex plane.