Computation of Tangent, Euler, and Bernoulli Numbers
نویسندگان
چکیده
منابع مشابه
Fast computation of Bernoulli, Tangent and Secant numbers
We consider the computation of Bernoulli, Tangent (zag), and Secant (zig or Euler) numbers. In particular, we give asymptotically fast algorithms for computing the first n such numbers in O(n2(logn)2+o(1)) bit-operations. We also give very short in-place algorithms for computing the first n Tangent or Secant numbers in O(n2) integer operations. These algorithms are extremely simple, and fast fo...
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Let [x] be the integral part of x. Let p > 5 be a prime. In the paper we mainly determine P[p/4] x=1 1 xk (mod p2), p−1 [p/4] (mod p3), Pp−1 k=1 2 k (mod p3) and Pp−1 k=1 2 k2 (mod p2) in terms of Euler and Bernoulli numbers. For example, we have
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1967
ISSN: 0025-5718
DOI: 10.2307/2005010