Higher-order recurrences for Bernoulli numbers
نویسندگان
چکیده
منابع مشابه
Congruences and Recurrences for Bernoulli Numbers of Higher Order
In particular, B^\0) = B^\ the Bernoulli number of order k, and BJp = Bn, the ordinary Bernoulli number. Note also that B^ = 0 for n > 0. The polynomials B^\z) and the numbers B^ were first defined and studied by Niels Norlund in the 1920s; later they were the subject of many papers by L. Carlitz and others. For the past twenty-five years not much has been done with them, although recently the ...
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In particular, the values at x = 0 are called Bernoulli numbers of order k, that is, Bn (0) = Bn k) (see [1, 2, 4, 5, 9, 10, 14]). When k = 1, the polynomials or numbers are called ordinary. The polynomials Bn (x) and numbers Bn were first defined and studied by Norlund [9]. Also Carlitz [2] and others investigated their properties. Recently they have been studied by Adelberg [1], Howard [5], a...
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Suppose X , Y are manifolds, f ,g : X → Y are maps. The well-known coincidence problem studies the coincidence set C = {x : f (x) = g(x)}. The number m= dimX −dimY is called the codimension of the problem. More general is the preimage problem. For a map f : X → Z and a submanifold Y of Z, it studies the preimage set C = {x : f (x) ∈ Y}, and the codimension is m = dimX + dimY − dimZ. In case of ...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2009
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2009.02.015